TI-86 Guidebook - Mathematics | Oregon State University

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TI-86 GRAPHING CALCULATOR GUIDEBOOK

TI-GRAPH LINK, Calculator-Based Laboratory, CBL, CBL 2, Calculator-Based Ranger, CBR, Constant Memory, Automatic Power Down, APD, and EOS are trademarks of Texas Instruments Incorporated. Windows is a registered trademark of Microsoft Corporation. IBM is a registered trademark of International Business Machines Corporation Macintosh is a registered trademark of Apple Computer, Inc. Copyright © 1997, 2001 by Texas Instruments Incorporated

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ii Important Texas Instruments makes no warranty, either expressed or implied, including but not limited to any implied warranties of merchantability and fitness for a particular purpose, regarding any programs or book materials and makes such materials available solely on an “as-is” basis. In no event shall Texas Instruments be liable to anyone for special, collateral, incidental, or consequential damages in connection with or arising out of the purchase or use of these materials, and the sole and exclusive liability of Texas Instruments, regardless of the form of action, shall not exceed the purchase price of this equipment. Moreover, Texas Instruments shall not be liable for any claim of any kind whatsoever against the use of these materials by any other party.

US FCC Information Concerning Radio Frequency Interference This equipment has been tested and found to comply with the limits for a Class B digital device, pursuant to Part 15 of the FCC rules. These limits are designed to provide reasonable protection against harmful interference in a residential installation. This equipment generates, uses, and can radiate radio frequency energy and, if not installed and used in accordance with the instructions, may cause harmful interference with radio communications. However, there is no guarantee that interference will not occur in a particular installation. If this equipment does cause harmful interference to radio or television reception, which can be determined by turning the equipment off and on, you can try to correct the interference by one or more of the following measures: ♦ Reorient or relocate the receiving antenna. ♦ Increase the separation between the equipment and receiver. ♦ Connect the equipment into an outlet on a circuit different from that to which the receiver is connected. ♦ Consult the dealer or an experienced radio/television technician for help.

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Table of Contents TI-86 Quick Start

1

Preparing to Use Your New TI-86 ..................................................... 2 Installing the AAA Batteries ......................................................... 2 Turning On and Turning Off the TI-86.......................................... 2 Adjusting the Contrast ................................................................. 2 Resetting All Memory and Defaults.............................................. 3 Calculating on the Home Screen....................................................... 3 Calculating the Sine of a Number................................................. 3 Storing the Last Answer to a Variable.......................................... 3 Using a Variable in an Expression ................................................ 4 Editing an Expression ................................................................... 4 Displaying a Complex Number as a Result................................... 5 Using a List with a Function ......................................................... 5 Displaying the Integer Part of Real Numbers in a List .................. 6 Removing (Exiting) a Menu.......................................................... 6 Finding the Square Root............................................................... 7 Calculating Derivatives................................................................. 7 Retrieving, Editing, and Re-evaluating the Previous Entry ........... 8 Converting Degrees Fahrenheit to Degrees Celsius...................... 8 Storing an Unevaluated Expression to an Equation Variable ....... 9 Plotting Functions on the Graph Screen............................................ 9

Displaying and Entering Functions in the Equation Editor............9 Changing the Graph Style of a Function.....................................10 Plotting a Function on the Graph Screen....................................11 Tracing a Function......................................................................11 Evaluating y for a Specific x Value (During a Trace) ...................12 Changing a Window Variable Value...........................................12 Deselecting a Function ...............................................................13 Zooming In on a Portion of the Graph Screen ............................14

Chapter 1: Operating the TI-86

15

Installing or Replacing Batteries .....................................................16 When to Replace Batteries .........................................................16 Turning On and Turning Off the TI-86.............................................17 Adjusting the Display Contrast........................................................17 The Home Screen ............................................................................18 Displaying Entries and Answers..................................................18 Entering Numbers ...........................................................................19 Entering Negative Numbers .......................................................19 Using Scientific or Engineering Notation....................................20 Entering Complex Numbers........................................................20 Entering Other Characters...............................................................21 The 2nd Key................................................................................21

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TI-86 Table of Contents

The ALPHA Key........................................................................... 21 ALPHA-lock and alpha-lock........................................................ 22 Common Cursors........................................................................ 22 Cursor Direction Keys ................................................................. 23 Inserting, Deleting, and Clearing Characters.............................. 23 Entering Expressions and Instructions ............................................ 24 Entering an Expression............................................................... 24 Using Functions in Expressions .................................................. 25 Using an Instruction ................................................................... 25 Entering Functions, Instructions, and Operators ........................ 25 Entering Consecutive Entries...................................................... 26 The Busy Indicator...................................................................... 26 Interrupting a Calculation or Graph ........................................... 26 Diagnosing an Error ........................................................................ 27 Correcting an Error..................................................................... 27 Reusing Previous Entries and the Last Answer ............................... 28 Retrieving the Last Entry ............................................................ 28 Retrieving and Editing the Last Entry ......................................... 28 Retrieving Previous Entries......................................................... 28 Retrieving Multiple Entries ......................................................... 29 Clearing the ENTRY Storage Area .............................................. 29 Retrieving the Last Answer ........................................................ 29 Using Ans Preceding a Function................................................. 30 Storing Results to a Variable ...................................................... 30 Using TI-86 Menus.......................................................................... 31

Displaying a Menu......................................................................31 The Menu Keys...........................................................................32 Selecting a Menu Item................................................................32 Exiting (Removing) a Menu ........................................................33 Viewing and Changing Modes ........................................................34 Changing a Mode Setting...........................................................34

Chapter 2: The CATALOG, Variables, and Characters

37

The CATALOG .................................................................................38 Storing Data to Variables ................................................................39 Creating a Variable Name ..........................................................39 Storing a Value to a Variable Name ...........................................40 Storing an Unevaluated Expression............................................40 Storing an Answer ......................................................................41 Copying a Variable Value ...........................................................41 Displaying a Variable Value........................................................41 Recalling a Variable Value..........................................................42 Classifying Variables as Data Types. ...............................................42 The CATLG-VARS (CATALOG-Variables) Menu...........................43 Selecting a Variable Name .........................................................44 The CUSTOM Menu.........................................................................44 Entering CUSTOM Menu Items...................................................44 Clearing CUSTOM Menu Items...................................................45 Deleting a Variable from Memory ..............................................45

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TI-86 Table of Contents The CHAR (Character) Menu........................................................... 45 The CHAR MISC (Miscellaneous) Menu...................................... 46 The CHAR GREEK Menu ............................................................. 46 The CHAR INTL (International) Menu ......................................... 46 Adding a Modifier to a Vowel .................................................... 46

Chapter 3: Math, Calculus, and Test Operations

47

Keyboard Mathematical Functions ................................................. 48 The MATH Menu............................................................................. 49 The MATH NUM (Number) Menu............................................... 49 The MATH PROB (Probability) Menu .......................................... 50 The MATH ANGLE Menu ............................................................ 51 The MATH HYP (Hyperbolic) Menu............................................. 51 The MATH MISC (Miscellaneous) Menu..................................... 52 The InterpolateàExtrapolate Editor ............................................ 53 The CALC (Calculus) Menu.............................................................. 54 The TEST (Relational) Menu............................................................ 55 Using Tests in Expressions and Instructions ............................... 56

Chapter 4: Constants, Conversions, Bases, and Complex Numbers

57

Using Built-In and User-Created Constants..................................... 58 The CONS (Constants) Menu...................................................... 58 The CONS BLTIN (Built-In Constants) Menu............................... 58

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Creating or Redefining a User-Created Constant .......................60 The Constant Editor Menu..........................................................60 Entering a Constant Name in an Expression ..............................61 Converting Units of Measure ..........................................................61 Converting a Unit of Measure ....................................................61 The CONV (Conversions) Menu ..................................................62 The CONV LNGTH (Length) Menu ..............................................63 The CONV AREA Menu...............................................................63 The CONV VOL (Volume) Menu..................................................63 The CONV TIME Menu................................................................63 The CONV TEMP (Temperature) Menu .......................................63 The CONV MASS Menu ..............................................................64 The CONV FORCE Menu .............................................................64 The CONV PRESS (Pressure) Menu .............................................64 The CONV ENRGY (Energy) Menu ..............................................64 The CONV POWER Menu............................................................64 The CONV SPEED Menu .............................................................64 Converting a Value Expressed as a Rate ....................................65 Number Bases .................................................................................65 Number Base Ranges .................................................................66 One’s and Two’s Complements ..................................................66 The (Number) BASE Menu..........................................................66 The BASE Õ-Ú (Hexadecimal Characters) Menu .........................67 Entering Hexadecimal Digits.......................................................67 The BASE TYPE Menu.................................................................67

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TI-86 Table of Contents

The BASE CONV (Conversion) Menu .......................................... 68 Converting Number Bases.......................................................... 68 The BASE BOOL (Boolean) Menu ............................................... 68 Results of Boolean Operations ................................................... 69 The BASE BIT Menu.................................................................... 69 Using Complex Numbers................................................................. 70 Complex Results......................................................................... 70 Using a Complex Number in an Expression................................ 71 The CPLX (Complex Number) Menu ........................................... 71

Chapter 5: Function Graphing

73

Defining a Graph............................................................................. 74 Setting the Graph Mode ................................................................. 74 The GRAPH Menu ........................................................................... 75 Using the Equation Editor ............................................................... 76 The Equation Editor (GRAPH y(x)=) Menu ................................. 76 Defining a Function in the Equation Editor ................................ 77 Notes about Defining Function Equations.................................. 78 Selecting Graph Styles................................................................ 79 Setting the Graph Style in the Equation Editor........................... 80 Using Shading Patterns to Differentiate Functions..................... 80 Viewing and Changing OnàOff Status of Stat Plots ................... 81 Setting the Window Variables......................................................... 81 Displaying the Window Editor.................................................... 82 Changing a Window Variable Value........................................... 82

Setting Graphing Accuracy with @x and @y ...............................83 Setting the Graph Format................................................................83 Displaying a Graph..........................................................................85 Pausing or Stopping a Graph in Progress ...................................85 Modifying a Drawn Graph ..........................................................85 Graphing a Family of Curves ......................................................86 Smart Graph ...............................................................................86

Chapter 6: Graph Tools

87

Graph Tools on the TI-86 ................................................................88 The GRAPH Menu.......................................................................88 Using the Free-Moving Cursor....................................................89 Graphing Accuracy .....................................................................89 Tracing a Graph...............................................................................90 Stopping and Resuming a Trace .................................................91 Resizing the Graph Screen with ZOOM Operations.........................91 The GRAPH ZOOM Menu ...........................................................91 Defining a Custom Zoom In........................................................93 Setting Zoom Factors..................................................................93 Zooming In and Zooming Out on a Graph..................................93 Storing and Recalling Zoom Window Variable Values................95 Using Interactive Math Functions ...................................................95 The GRAPH MATH Menu............................................................95 Settings That Affect GRAPH MATH Operations ..........................96 Using ROOT, FMIN, FMAX, or INFLC ..........................................97

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TI-86 Table of Contents Using ‰f(x), DIST, or ARC ............................................................ 98 Using dyàdx or TANLN............................................................... 99 Using ISECT .............................................................................. 100 Using YICPT.............................................................................. 100 Evaluating a Function for a Specified x......................................... 101 Drawing on a Graph...................................................................... 101 Before Drawing on a Graph ..................................................... 102 Saving and Recalling Drawn Pictures ....................................... 102 Clearing Drawn Pictures........................................................... 103 The GRAPH DRAW Menu ......................................................... 103 Shading Areas of a Graph ........................................................ 104 Drawing a Line Segment .......................................................... 105 Drawing a Vertical or Horizontal Line ...................................... 106 Drawing a Circle....................................................................... 106 Drawing a Function, Tangent Line, or Inverse Function ........... 107 Drawing Freehand Points, Lines, and Curves ........................... 107 Placing Text on a Graph ........................................................... 108 Turning On or Turning Off Points ............................................. 108

Chapter 7: Tables

109

Displaying the Table...................................................................... 110 TABLE Menu............................................................................. 110 The Table.................................................................................. 110 Independent and Dependent Variables in the Table ................ 111 Navigating the Table................................................................ 111

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The Table Menus ......................................................................112 Setting Up the Table .....................................................................113 Viewing and Editing Dependent Variable Equations ...............114 Clearing the Table .........................................................................114

Chapter 8: Polar Graphing

115

Preview: Polar Graphing ...............................................................116 Defining a Polar Graph..................................................................117 Setting Polar Graphing Mode ...................................................117 The GRAPH Menu.....................................................................117 Displaying the Polar Equation Editor ........................................118 Setting the Graph Screen Window Variables............................118 Setting the Graph Format.........................................................119 Displaying the Graph................................................................119 Using Graph Tools in Pol Graphing Mode .....................................119 The Free-Moving Cursor ...........................................................119 Tracing a Polar Equation ..........................................................120 Moving the Trace Cursor to a q Value......................................121 Using Zoom Operations............................................................121 The GRAPH MATH Menu..........................................................122 Evaluating an Equation for a Specified q..................................122 Drawing on a Polar Graph........................................................122

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TI-86 Table of Contents

Chapter 9: Parametric Graphing

123

Preview: Parametric Graphing ...................................................... 124 Defining a Parametric Graph......................................................... 125 Setting Parametric Graphing Mode.......................................... 126 The GRAPH Menu..................................................................... 126 Displaying the Parametric Equation Editor............................... 126 Selecting and Deselecting a Parametric Equation .................... 127 Deleting a Parametric Equation................................................ 127 Setting the Graph Screen Window Variables............................ 127 Setting the Graph Format......................................................... 128 Displaying the Graph................................................................ 128 Using Graph Tools in Param Graphing Mode................................ 128 The Free-Moving Cursor........................................................... 128 Tracing a Parametric Function.................................................. 128 Moving the Trace Cursor to a t Value....................................... 129 Using Zoom Operations............................................................ 129 The GRAPH MATH Menu.......................................................... 130 Evaluating an Equation for a Specified t .................................. 130 Drawing on a Parametric Graph............................................... 130

Chapter 10: Differential Equation Graphing 131 Defining a Differential Equation Graph......................................... 132 Setting Differential Equation Graphing Mode .......................... 132 The GRAPH Menu..................................................................... 133 Setting the Graph Format......................................................... 133

Displaying the Differential Equation Editor ..............................134 Setting the Graph Screen Window Variables............................135 Setting the Initial Conditions....................................................136 Setting the Axes .......................................................................137 Differential Equation Graphing Tips .........................................137 The Built-In Variable fldPic .......................................................138 Displaying the Graph................................................................138 Entering and Solving Differential Equations..................................139 Graphing in SlpFld Format........................................................139 Transforming an Equation into a First-Order System................140 Graphing in DirFld Format ........................................................141 Graphing a System of Equations in FldOff Format....................142 Solving a Differential Equation for a Specified Value ...............144 Using Graph Tools in DifEq Graphing Mode .................................144 The Free-Moving Cursor ...........................................................144 Tracing a Differential Equation.................................................144 Moving the Trace Cursor to a t Value.......................................145 Drawing on a Differential Equation Graph ...............................145 Drawing an Equation and Storing Solutions to Lists.................145 Using ZOOM Operations...........................................................147 Drawing Solutions Interactively with EXPLR.............................148 Evaluating Differential Equations for a Specified t ...................150

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TI-86 Table of Contents

Chapter 11: Lists

151

Lists on the TI-86 .......................................................................... 152 The LIST Menu.......................................................................... 152 The LIST NAMES Menu............................................................. 153 Creating, Storing, and Displaying Lists.......................................... 153 Entering a List Directly in an Expression................................... 153 Creating a List Name by Storing a List ..................................... 154 Displaying List Elements Stored to a List Name ....................... 154 Displaying or Using a Single List Element ................................ 155 Storing a New Value to a List Element..................................... 155 Complex List Elements ............................................................. 156 The List Editor ............................................................................... 156 The List Editor Menu ................................................................ 156 Creating a List Name in the Unnamed Column ........................ 157 Inserting a List Name into the List Editor ................................. 157 Displaying and Editing a List Element ...................................... 158 Deleting Elements from a List .................................................. 158 Removing a List from the List Editor ........................................ 158 Using List Operations.................................................................... 159 The LIST OPS (Operations) Menu ............................................. 159 Using Mathematical Functions with Lists ..................................... 161 Attaching a Formula to a List Name ............................................. 162 Comparing an Attached List with a Regular List ...................... 163 Using the List Editor to Attach a Formula ................................ 163 Using the List Editor With Attached-Formula Lists ................... 164

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Executing and Displaying Attached Formulas ..........................164 Handling Errors Related to Attached Formulas.........................165 Detaching a Formula from a List Name ....................................166 Editing an Element of a Attached Formula List ........................166

Chapter 12: Vectors

167

Vectors on the TI-86 .....................................................................168 Creating, Storing, and Displaying Vectors.....................................169 The VECTR (Vector) Menu ........................................................169 The VECTR NAMES Menu.........................................................169 Creating a Vector in the Vector Editor......................................169 The Vector Editor Menu............................................................170 Creating a Vector on the Home Screen.....................................170 Creating a Complex Vector.......................................................171 Displaying a Vector...................................................................171 Using a Vector in an Expression ...............................................172 Editing Vector Dimension and Elements...................................172 The VECTR MATH Menu...........................................................173 The VECTR OPS (Operations) Menu..........................................173 The VECTR CPLX (Complex) Menu ...........................................175 Using Mathematical Functions with Vectors.................................176

Chapter 13: Matrices

177

Matrices on the TI-86....................................................................178 Creating, Storing, and Displaying Matrices ...................................178

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TI-86 Table of Contents

The MATRX (Matrix) Menu ...................................................... 178 The MATRX NAMES Menu ....................................................... 178 Creating a Matrix in the Matrix Editor ..................................... 178 The Matrix Editor Menu ........................................................... 179 Creating a Matrix on the Home Screen .................................... 180 Creating a Complex Matrix ...................................................... 180 Displaying Matrix Elements, Rows, and Submatrices............... 181 Using a Matrix in an Expression............................................... 181 Editing Matrices in the Matrix Editor ....................................... 182 Editing Matrices on the Home Screen ...................................... 182 The MATRX MATH Menu ......................................................... 183 The MATRX OPS (Operations) Menu ........................................ 184 The MATRX CPLX (Complex ) Menu......................................... 185 Using Mathematical Functions with Matrices............................... 185

Chapter 14: Statistics

187

Statistical Analysis on the TI-86.................................................... 188 Setting Up a Statistical Analysis.................................................... 188 The STAT (Statistics) Menu....................................................... 188 Entering Statistical Data........................................................... 189 The LIST NAMES Menu............................................................. 189 The STAT CALC (Calculations) Menu........................................ 189 Automatic Regression Equation Storage .................................. 191 Results of a Statistical Analysis..................................................... 192 The STAT VARS (Statistical Variables) Menu ............................ 192

Plotting Statistical Data.................................................................194 The STAT PLOT Status Screen...................................................194 The STAT PLOT Menu ...............................................................195 Setting Up a Stat Plot ...............................................................195 Turning On and Turning Off a Stat Plot ....................................195 The PLOT TYPE Menu (Selecting a Plot Type)...........................196 Plot Type Characteristics ..........................................................196 The STAT DRAW Menu..................................................................199 Forecasting a Statistical Data Value..............................................199

Chapter 15: Equation Solving

201

Preview: The Equation Solver........................................................202 Entering an Equation in the Equation-Entry Editor........................203 Setting Up the Interactive-Solver Editor ........................................204 Entering Variable Values ..........................................................204 Controlling the Solution with Bounds and a Guess ..................204 Editing the Equation.................................................................205 The Solver Menu.......................................................................206 Solving for the Unknown Variable ................................................206 Graphing the Solution ...................................................................207 Solver Graph Tools ........................................................................207 The Solver ZOOM Menu ...........................................................208 The Simultaneous Equation Solver................................................208 Entering Equations to Solve Simultaneously ............................208 Storing Equation Coefficients and Results to Variables............210 The Polynomial Root-Finder ..........................................................211

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TI-86 Table of Contents Entering and Solving a Polynomial........................................... 211 Storing a Polynomial Coefficient or Root to a Variable ............ 212

Chapter 16: Programming

213

Writing a Program on the TI-86 .................................................... 214 The PRGM Menu ...................................................................... 214 Creating a Program in the Program Editor ............................... 214 The Program Editor Menu ........................................................ 215 The PRGM IàO (InputàOutput) Menu ...................................... 215 The TI-86 Key Code Diagram ................................................... 217 The PRGM CTL Menu ............................................................... 218 Entering a Command Line ........................................................ 220 Menus and Screens in the Program Editor ............................... 220 Running a Program ....................................................................... 221 Breaking (Interrupting) a Program ........................................... 222 Working with Programs ................................................................ 223 Managing Memory and Deleting a Program ............................ 223 Editing a Program..................................................................... 223 Calling a Program from Another Program................................ 224 Copying a Program to Another Program Name........................ 225 Using and Deleting Variables within a Single Program ............ 225 Running an Assembly Language Program .................................... 225 Entering and Storing a String........................................................ 226 The STRNG (String) Menu ........................................................ 227 Creating a String ...................................................................... 227

Chapter 17: Memory Management

xi 229

Checking Available Memory .........................................................230 The MEM (Memory) Menu .......................................................230 Checking Memory Usage..........................................................230 Deleting Items from Memory ........................................................231 The MEM DELET (Delete) Menu ...............................................231 Resetting the TI-86 .......................................................................232 The MEM RESET (Reset) Menu.................................................232 ClrEnt (Clear Entry)...................................................................232

Chapter 18: The TI-86 Communication Link

233

TI-86 Linking Options....................................................................234 Linking Two TI-86s ...................................................................234 Linking a TI-86 and a TI-85......................................................234 Linking a TI-86 and a CBL 2/CBL or CBR System......................234 Linking a TI-86 and a PC or Macintosh ....................................235 Downloading Programs from the Internet................................235 Connecting the TI-86 to Another Device.......................................235 The LINK Menu.........................................................................236 Selecting Data to Send ..................................................................236 The LINK SEND Menu ...............................................................236 Initiating a Memory Backup .....................................................237 Selecting Variables to Send ......................................................238 The SEND WIND (Window Variables) Screen............................238 Sending Variables to a TI-85 ....................................................239

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TI-86 Table of Contents

The LINK SND85 (Send Data to TI-85) Menu ........................... 239 Preparing the Receiving Device..................................................... 240 Transmitting Data ......................................................................... 240 Receiving Transmitted Data .......................................................... 241 Repeating Transmission to Several Devices ............................. 242 Error Conditions ....................................................................... 242 Insufficient Memory in Receiving Unit...................................... 242

Chapter 19: Applications

243

Using Math Operations with Matrices .......................................... 244 Finding the Area between Curves ................................................. 245 The Fundamental Theorem of Calculus......................................... 246 Electrical Circuits........................................................................... 248 Program: Taylor Series .................................................................. 250 Characteristic Polynomial and Eigenvalues................................... 252 Convergence of the Power Series ................................................. 254 Reservoir Problem......................................................................... 256 Predator-Prey Model ..................................................................... 258 Program: Sierpinski Triangle ......................................................... 260

Chapter 20: A to Z Function and Instruction Reference

Appendix

379

TI-86 Menu Map ...........................................................................380 Handling a Difficulty......................................................................392 Error Conditions ............................................................................393 Equation Operating System (EOSé)..............................................397 Implied Multiplication ..............................................................397 Parentheses ..............................................................................397 TOL (The Tolerance Editor)............................................................398 Computational Accuracy ...............................................................399 Support and Service Information...................................................400 Product Support........................................................................400 Product Service.........................................................................401 Other TI Products and Services .................................................401 Warranty Information....................................................................402 Customers in the U.S. and Canada Only...................................402 Australia & New Zealand Customers Only................................403 All Customers outside the U.S. and Canada .............................404

Index 261

Quick-Find Locator........................................................................ 262 Alphabetical Listing of Operations................................................ 266

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TI-86 Quick Start TI-86

Preparing to Use Your New TI-86 ........................................ 2 Calculating on the Home Screen.......................................... 3 Plotting Functions on the Graph Screen .............................. 9

M1

M2

M3

M4

M5

F1

F2

F3

F4

F5

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2

Quick Start

Preparing to Use Your New TI-86 The brief examples in the TI-86 Quick Start demonstrate some common TI-86 features. Before you begin, you must install the batteries, turn on the calculator, adjust the contrast, and reset the memory and the defaults. Chapter 1 has more details on these topics. Installing the AAA Batteries Four AAA batteries are included in the TI-86 retail package. Remove the batteries from the package and install them in the battery compartment on the back of the calculator. Arrange the batteries according to the polarity (+ and N) diagram in the battery compartment.

After about four minutes of inactivity, the TI-86 turns off automatically.

Turning On and Turning Off the TI-86 To turn on the TI-86, press ^, which is in the bottom-left corner of the keyboard. You should see the entry cursor ( Å ) blinking in the top-left corner of the screen. If you do not see it, adjust the contrast (see below).

RCL

ST O OFF

ON

To turn off the calculator, press -, and then the key under OFF, which is ^. This guidebook uses brackets ( ã and ä ) to express - and 1 keystroke combinations. For example, to turn off the TI-86, press - ž. Adjusting the Contrast If you release $ or # while adjusting the contrast, you must press - again to continue the adjustment.



Press and release the yellow - key. Press and hold $ or # (above or below the half-shaded circle). ♦ To darken the screen contrast, press and hold $. ♦ To lighten the screen contrast, press and hold #.

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MODE

QUIT

2nd alpha

ALPHA

EXIT LINK

x-VAR

MORE x

INS

DEL

=

BASE U

1 CHAR Y

0

Quick Start

3

Resetting All Memory and Defaults To reset all memory and defaults, press - ™ ( & ). The messages Mem cleared and Defaults set are displayed on the home screen, confirming that all memory and defaults are reset. You may need to adjust the contrast after memory and default reset.

Calculating on the Home Screen To express - and 1 keystroke combinations, this guidebook places brackets ( ã and ä ) around the word above the key to press.

To replicate the screens shown in the Quick Start activities, reset all memory and defaults once before you begin. Before doing an activity, press : to clear the screen (except before the entry retrieval and integer-part examples). Otherwise, the screens your TI-86 shows may differ from the screens pictured next to the activities. Calculating the Sine of a Number

The TI-86 on-screen division symbol is a forward slash ( à ), as in a fraction.



Enter the sine function.

(:) =



Enter a value. You can enter an expression, which is evaluated when you press b.

D -~F4E

Following evaluation, the entry cursor automatically moves to the next line, ready for a new entry.



Evaluate the problem. The evaluation of the expression sine(pà4) is displayed.

b

Storing the Last Answer to a Variable When the TI-86 evaluates an expression, it automatically stores the answer to the builtin variable Ans, replacing any previous value.



Paste the store symbol ( ¶ ) to the screen. Since a value must precede ¶ , but you did not enter a value, the TI-86 automatically pasted Ans before ¶. (continued)

(:) X

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Quick Start

When ALPHA-lock is on and you press a key, the letters printed in blue above the keys are pasted to the screen. In the example, press Z to enter a V.



Enter the variable name to which you want to store the last answer. ALPHA-lock is on.

ãVä



Store the last answer to the variable. The stored value is displayed on the next line.

b

Using a Variable in an Expression

Enter the variable, and then square it.

(:) 1 ãVä I



Evaluate. The value stored to the variable V is squared and displayed.

b

Editing an Expression

You need not move the cursor to the end of the line to evaluate the expression.



Enter the expression (25+14)(4N3.2).

(:) D 25 \ 14 E D4T3`2E



Change 3.2 to 2.3.

!!!!2"3



Move the cursor to the beginning of the expression and insert a value. The insert cursor blinks between 3 and 25.

-!-p3



Evaluate. The result is displayed.

b

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Quick Start

a negates a value, as in L2. T subtracts, as in 5N2=3.

An ellipsis (...) indicates that the result continues beyond the screen.

Displaying a Complex Number as a Result

Enter the natural log function.

(:) B



Enter a negative number.

Da2E



Evaluate. The result is displayed as a complex number.

b (press " to display more)

Using a List with a Function

Enter the exponential function.

(:) - ‚



Display the LIST menu, and then select the open brace ( { ) from the LIST menu.

-” &

On the TI-86, { specifies the beginning of a list.

LIST menu



Enter the list elements. Separate each element from the next with a comma.

5 P 10 P 15



Select the close brace ( } ) from the LIST menu to specify the end of the list.

'



Evaluate. The results of the constant e raised to the 5th, 10th, and 15th powers are displayed as list elements.

b (press " to display more)

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5

6

Quick Start

Displaying the Integer Part of Real Numbers in a List

Display the MATH menu. (The MATH menu automatically replaces the LIST menu from the last activity.)





Select NUM to display the MATH NUM menu. The MATH menu shifts up.

&



Select the iPart (integer part) function from the MATH NUM menu. iPart is pasted to the screen. (The previous entry was left on the screen to illustrate the effect of iPart on the previous answer.)

'



Paste Ans to the cursor location. (The result list from the previous activity is stored to Ans.)





Display the integer part of the result list elements from the previous activity.

b

MATH menu MATH NUM menu

Removing (Exiting) a Menu

In the previous example, the MATH menu and the MATH NUM menu are displayed (- Π&).



Remove the MATH NUM menu from the screen.

.



Remove the MATH menu from the screen.

.

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Quick Start

Finding the Square Root

Paste the square root function to the screen.

(:) - ˆ



Enter a value for which you want to find the square root.

144



Evaluate the expression. The square root of 144 is displayed.

b

Calculating Derivatives

Display the CALC menu, and then select der1.

(:) -† ( CALC menu



Enter an expression ( x 2) with respect to a variable (x) at a given point (8).

2IP2 P8E



Evaluate. The first derivative of x 2 with respect to x at 8 is displayed.

b

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7

8

Quick Start

Retrieving, Editing, and Re-evaluating the Previous Entry When you press b, the TI-86 stores the expression or instruction you entered to the built-in memory storage area called ENTRY.



Retrieve the last entry from the previous example. (The last activity was not cleared.)





Edit the retrieved entry.

!!3



Evaluate. The first derivative of x 2 with respect to x at 3 is displayed.

b

Converting Degrees Fahrenheit to Degrees Celsius

When expressing a measurement for a conversion, you do not enter a unit symbol manually. For example, you need not enter ¡ to designate degrees.



Display the CONV menu.

(:) - ’



Display the CONV TEMP menu. The CONV menu shifts up and TEMP is highlighted.

*



Enter the known measurement. If the measurement is negative, use parentheses. In this example, if you omit parentheses, the TI-86 converts 4¡F to about L15.5¡C, which it then negates (changes the sign of), returning a positive 15.5¡C.

Da4E



Select ¡F to designate Fahrenheit as the known measurement unit. ¡F and the conversion symbol ( 4 ) are displayed after the measurement. (continued)

'

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Quick Start

Select ¡C to designate Celsius as the unit to which you want to convert.

&



Convert. The ¡C equivalent of L4¡F is displayed.

b

9

Storing an Unevaluated Expression to an Equation Variable When storing to an equation variable using =, enter the equation variable first, then =, and then the unevaluated expression. This is the opposite from the order for storing to most other variables on the TI-86.



Enter the built-in equation variable y1.

(:) - n ãYä 1



Enter the equals sign (=).

1 ã=ä



Enter an expression in terms of x.

5D=2E



Store the expression.

b

The next section shows how to graph the functions y1=5(sin x) and y2=5(cos x).

Plotting Functions on the Graph Screen The TI-86 plots four types of functions on the graph screen. To plot a graph, you must store an unevaluated expression to a built-in equation variable. Each activity in this section builds upon the activity that precedes it. You must start here and perform the activities in the sequence in which they are presented. The first activity in this section assumes you are continuing from the last activity in the previous section. Displaying and Entering Functions in the Equation Editor

Display the GRAPH menu.

(continued)

6

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10

Quick Start

In the equation editor, you must express each equation in terms of the independent variable x (in Func graphing mode only; Chapter 5).



Select y(x)= from the GRAPH menu to display the equation editor. 5(sin x) is the unevaluated expression stored to y1 in the previous activity. The equation editor menu is displayed as the lower menu.

&



Move the cursor down. The y2= prompt is displayed.

#



Enter the expression 5(cos x) at the y2= prompt. Notice that the equals sign (=) of y2 is highlighted after you enter 5. Also, the equals sign of y1 is highlighted. This indicates that both equations are selected to be graphed (Chapter 5).

5D>2E

equation editor menu

Changing the Graph Style of a Function In the equation editor, the icon to the left of each equation specifies the style in which the graph of that equation appears when you plot it on the graph screen.

To display up to seven graph styles, depending on the graphing mode, repeat (.



Move the cursor to y1.

$



Display the next menu group of the equation editor menu. ( 4 at the end of a menu group indicates that the menu has more items.)

/



Select STYLE from the equation editor menu to set ¼ (thick) graph style for y1.

( graph style icons

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Quick Start

11

Plotting a Function on the Graph Screen

Select GRAPH from the GRAPH menu to plot the graph on the graph screen. The xand y-axes and GRAPH menu are displayed. Then each selected graph is plotted in the order in which it is listed in the equation editor.

-i



When the graph is plotted, you can move the free-moving cursor ( + ) around the graph screen. The cursor coordinates are displayed at the bottom of the graph.

"#!$

free-moving cursor

Tracing a Function

Select TRACE from the GRAPH menu to activate the trace cursor, with which you can trace along the graph of any selected function. The number of the current function (the 1 in y1) is displayed in the top-right corner.

)



Move the trace cursor from the function y1 to the function y2. The 1 in the top-right corner changes to 2; the y value changes to the value of y2 at x=0. (continued)

$

trace cursor

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12

Quick Start

Trace the function y2. As you trace, the displayed y value is the solution for 5(cos x) at the current x value, which also is displayed on the screen.

" and !

Evaluating y for a Specific x Value (During a Trace)

Enter a real number (or an expression that resolves to a real number) that is within the dimensions of the current graph screen. When you enter the first character, the x= prompt is displayed.

6



Evaluate y2 at x=6. The trace cursor moves directly to the solution. The y value, or solution of the equation at x, is displayed on the screen.

b

Changing a Window Variable Value The window variables values determine the dimensions of the graph screen.



Display the GRAPH menu.

6



Select WIND from the GRAPH menu to display the window editor.

'

(continued)

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Quick Start

Change the value stored in the xMin window variable to 0.

0



Plot the graph on the redefined graph screen. Since xMin=0, only the first and fourth quadrants of the graph plane are displayed.

*

Deselecting a Function

Select y(x)= from the GRAPH menu to display the equation editor and equation editor menu. The GRAPH menu shifts up and y(x)= is highlighted.

&



Select SELCT from the equation editor menu to deselect the function y1=. The equals sign is no longer highlighted.

*



Plot the graph on the graph screen. Since you deselected y1, the TI-86 only plots y2. To select a function in the equation editor, repeat these steps. (SELCT both selects and deselects functions.)

-i

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13

14

Quick Start

Zooming In on a Portion of the Graph Screen

Select ZOOM to display the GRAPH ZOOM menu. The GRAPH menu shifts up and ZOOM is highlighted.

(



Select BOX from the GRAPH ZOOM menu to activate the zoom-box cursor.

&



Move the zoom-box cursor to a point that is to be a corner of the redefined graph screen, and then mark the point with a small square.

"#!$ b



Move the cursor away from the small square to a point that is to be the opposite corner of the redefined graph screen. As you move the cursor, a rectangle is drawn on the graph.

"#!$



Zoom in on the graph. The window variables change automatically to the specifications of the zoom box.

b



Clear the menus from the graph screen.

:

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1

Operating the TI-86 TI-86

Installing or Replacing Batteries ........................................ 16 Turning On and Turning Off the TI-86 ............................... 17 Adjusting the Display Contrast .......................................... 17 The Home Screen ............................................................... 18 Entering Numbers .............................................................. 19 Entering Other Characters ................................................. 20 Entering Expressions and Instructions ............................... 24 Diagnosing an Error ........................................................... 27 Reusing Previous Entries and the Last Answer .................. 28 Using TI-86 Menus ............................................................ 31 Viewing and Changing Modes........................................... 34

M1

M2

M3

M4

M5

F1

F2

F3

F4

F5

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16

Chapter 1: Operating the TI-86

Installing or Replacing Batteries Your new TI-86 includes four AAA alkaline batteries. You must install them before you can turn on the calculator. A lithium backup battery is installed in the calculator already. To express - and 1 keystroke combinations, this guidebook places brackets ( ã and ä ) around the word above the key to press.



If the calculator is on, turn it off (press - ž) to avoid loss of information stored in memory.



Slide the protective cover over the keyboard.



Holding the calculator upright, push down on the battery cover latch, and then remove the cover.

Do not remove the lithium backup battery unless four fresh AAA batteries are in place. Properly dispose of the old batteries.



Remove all four old batteries.

If you do not use your TI-86 frequently, the AAA batteries could last more than two weeks after the first lowbattery message.



Install four new AAA alkaline batteries, arranged according to the polarity (+ and N) diagram inside the battery compartment.



Replace the battery cover by inserting the two prongs into the two slots at the bottom of the battery compartment, and then push the cover until the latch snaps closed.

When to Replace Batteries When the AAA batteries are low, a low-battery message is displayed as you turn on the calculator. Generally, the calculator will continue to operate for one or two weeks after the low-battery message is first displayed. Eventually, the TI-86 will turn off automatically and will not operate until you replace the AAA batteries. The lithium backup battery is inside the battery compartment, above the AAA batteries. It retains all memory when the AAA batteries are low or have been removed. To avoid loss of data, do not remove the lithium battery unless four fresh AAA batteries are installed. Replace the lithium backup battery about every three or four years.

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17

Chapter 1: Operating the TI-86 Properly dispose of the old battery.

To replace the lithium backup battery, remove the battery cover and unscrew the tiny screw holding the BACK UP BATTERY cover in place. Install a new CR1616 or CR1620 battery according to the polarity (+ and N) diagram on the cover. Replace the cover and screw.

Turning On and Turning Off the TI-86 To turn on the TI-86, press ^. ♦ If you previously had turned off the calculator by pressing - ž, the TI-86 clears any errors and displays the home screen as it was last displayed. ♦ If Automatic Power DownTM (APDTM) previously had turned off the calculator, the TI-86 will return as you left it, including the display, cursor, and any error.

P

CONS Q

CONV R

4

5

, RCL

=

BASE U

OFF

TES T

1

ST O

CHAR Y

6 V

MEM

2 :

W

3 Z

ANS

( (

0

ON

STRNG S

To turn off the TI-86 manually, press - ž. All settings and memory contents are retained by the Constant Memory TM feature. Any error condition is cleared. APD turns off the TI-86 automatically after about four minutes of non-use to extend battery life.

Adjusting the Display Contrast If you release $ or # while adjusting the contrast, you must press - again to continue the adjustment.



Press and release the yellow - key. Press and hold $ or # (above or below the half-shaded circle). ♦ To darken the screen contrast, press and hold $. ♦ To lighten the screen contrast, press and hold #.

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MODE

QUIT

2nd alpha

ALPHA

EXIT LINK

x-VAR

MORE x

INS

DEL

18

Chapter 1: Operating the TI-86

The TI-86 has 40 contrast settings, so each number 0 through 9 represents four settings.

You can adjust the display contrast anytime to suit your viewing angle and lighting conditions. As you adjust, a number from 0 (lightest) to 9 (darkest) in the top-right corner indicates the current contrast setting. The number is not visible when the contrast is extremely light or dark. As the batteries weaken over time, the actual contrast level of each number shifts. For example, say you set the contrast to 3 with fresh batteries. As the batteries weaken, you will need to set the contrast to 4, then 5, then 6, and so on, to retain the original contrast level. However, you need not replace the batteries until the low-battery message is displayed.

The Home Screen When you first turn on your TI-86, the home screen is displayed. Initially, the home screen is a blank screen, except for the entry cursor ( Å ) in the top-left corner. If you do not see the cursor, press -, and then press and hold # or $ to adjust the contrast (page 17). On the home screen, you can enter and evaluate expressions, and view the results. You also can execute instructions, store and recall variable values, and set up graphs and editors. To return to the home screen from any other screen, press - l.

You need not clear the home screen to begin a new entry.

Displaying Entries and Answers The home screen displays up to eight lines with a maximum of 21 characters per line. If an expression or series of instructions exceeds 21 characters and spaces, it automatically continues on the next line. After all eight lines are full, text scrolls off the top of the display. You can press $ to scroll up the home screen, only as far as the first character in the current entry. To retrieve, edit, and re-execute previous entries, use - ¢ (page 28).

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Chapter 1: Operating the TI-86 The mode settings control the way the TI-86 interprets expressions and displays answers (page 34).

When an entry is executed on the home screen, the answer is displayed on the right side of the next line. When you execute an instruction, Done is typically displayed on the right side of the next line.

Entry Answer

If an answer is too long to display on the screen, an ellipsis (...) is displayed, initially to the right. To view more of the answer, press ". When you do, an ellipsis is displayed to the left. To scroll back, press !.

Entry Answer

19

Entering Numbers The TI-86 on-screen division symbol is a forward slash ( à ), as in a fraction.

A symbol or abbreviation of each key’s primary function is printed in white on the key. For example, when you press \, a plus sign is pasted to the cursor location. This guidebook describes number-entry keystrokes as 1, 2, 3, and so on, instead of Y Z [. Entering Negative Numbers To enter a negative number, press a (the negate key), and then press the appropriate number keys. For example, to enter L5, press a 5. Do not attempt to express a negative number using T (the subtract key). a and T are two different keys with different uses.

Always use parentheses to clarify negation when you use conversion instructions (Chapter 4).

The order in which the TI-86 evaluates negation and other functions within an expression is governed by the Equation Operating Systemè (Appendix). For example, the result of L4 2 is L16, while the result of (L4) 2 is 16. If you are unsure about the order of evaluation, use D and E to clarify the intended use of the negation symbol.

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20

Chapter 1: Operating the TI-86

Using Scientific or Engineering Notation

Enter the mantissa (part of the number that precedes the exponent). This value can be an expression.

D19 F2E



Paste E to the cursor location.

C

In scientific notation only, one digit precedes the decimal.



If the exponent is negative, paste L to the cursor location. Then enter a one-, two-, or three-digit exponent.

a2

In engineering notation, one, two, or three digits precede the decimal and the power of 10 exponent is a multiple of 3.



Evaluate the expression.

b

When you include scientific- or engineering-notation numbers in an expression, the TI-86 does not necessarily display answers in scientific or engineering notation. The mode settings (page 34) and the size of the number determine the notation of displayed answers. Entering Complex Numbers On the TI-86, the complex number a+bi is entered as (a,b) in rectangular complex-number form or as (rq ) in polar complex-number form. For more information about complex numbers, read Chapter 4.

Entering Other Characters MODE

QUIT

This is the 2nd key

2nd alpha

This is the ALPHA key

ALPHA

EXIT LINK

x-VAR

MORE x

INS

DEL

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Chapter 1: Operating the TI-86

The 2nd Key The - key is yellow. When you press -, the cursor becomes Æ (the 2nd cursor). When you press the next key, the yellow character, abbreviation, or word printed above that key is activated, instead of the key’s primary function.

To enter a space within text, press 1 ¤. Spaces are not valid within variable names.

The ALPHA Key The 1 key is blue. When you press 1, the cursor becomes ³ (the uppercase ALPHA cursor). When you press the next key, the blue uppercase character printed above that key is pasted to the cursor location.

For convenience, you can press 2 instead of n ãxä to enter the commonly used x variable.

When you press - n, the cursor becomes Ï (the lowercase alpha cursor). When you press the next key, the lowercase version of the blue character is pasted to the cursor location.

The Name= prompt and store symbol (¶) set ALPHA-lock automatically.

- š returns the STAT menu

STAT

X

STAT

X

STAT

21

X

1 ãXä returns an X

- n ãXä returns an x

ALPHA-lock and alpha-lock To enter more than one uppercase or lowercase alpha character consecutively, set ALPHAlock (for uppercase letters) or alpha-lock (for lowercase letters). To set ALPHA-lock when the entry cursor is displayed, press 1 1. ♦ To cancel ALPHA-lock, press 1. ♦ To switch from ALPHA-lock to alpha-lock, press - n. To set alpha-lock when the entry cursor is displayed, press - n 1. ♦ To cancel alpha-lock, press 1 1.

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22

Chapter 1: Operating the TI-86



To switch from alpha-lock to ALPHA-lock, press 1.

You can use - when ALPHA-lock or alpha-lock is on. Also, if you press a key that has no blue character above it, such as 6, 3, or !, the key’s primary function still applies. Common Cursors In most cases, the appearance of the cursor indicates what will happen when you press the next key. Graphs and editors sometimes use additional cursors, which are described in other chapters.

Entry

Å

Enters a character at the cursor, overwriting any existing character

Insert

__

Inserts a character at the cursor location and shifts remaining characters right

Second

Æ

Enters a 2nd character or executes a 2nd operation (yellow on the keyboard)

ALPHA

³

Enters an uppercase ALPHA character (blue on the keyboard)

alpha

Ï

Enters the lowercase version of an ALPHA character (blue on the keyboard)

Full

Ä

Accepts no data; maximum characters are entered at a prompt or memory is full

♦ ♦ ♦

If you press 1 after - p, the cursor becomes an underlined A (A). If you press - 1 after - p, the cursor becomes an underlined a (a). If you press - after - p, the insert cursor becomes an underlined # ( # ).

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Chapter 1: Operating the TI-86

23

Cursor Direction Keys - $ scrolls/moves cursor up - $ darkens screen contrast

! moves cursor left

" moves cursor right

- ! moves cursor to beginning of entry

- " moves cursor to end of entry

- # scrolls/moves cursor down - # lightens screen contrast

If you hold down ", #, !, or $, the cursor continues to move. Inserting, Deleting, and Clearing Characters The entry cursor ( Å ) overwrites characters.

-p

Changes the cursor to the insert cursor ( __ ); inserts characters at the insert cursor and shifts remaining characters right; to cancel insert, press - p or press ", #, !, or $

3

Deletes a character at the cursor; to continue deleting to the right, hold down 3

:

Clears the current entry on the home screen; : : clears the entire home screen

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24

Chapter 1: Operating the TI-86

Entering Expressions and Instructions Entering an Expression An expression is any combination of numbers and variables that serve as arguments for one or more functions. On the TI-86, you typically enter an expression in the same order as you would write it on paper. For example, pr 2, 5 tan xStat, and 40((L5+3)N(2+3)) are expressions. You can use an expression on the home screen to calculate an answer. In most places where a value is required, you can use an expression to enter the value. For example, enter an expression as a window variable value (Chapter 5). When you press #, $, b, or ., the TI-86 evaluates the expression and replaces it with the result. To enter an expression, you enter numbers, variables, and functions from the keyboard and menus (page 31). When you press b, the expression is evaluated (regardless of the cursor location) according to EOS order-of-evaluation rules (Appendix), and the answer is displayed. To enter the expression 3.76 ÷ (L7.9 + ‡5) + 2 log 45 and then evaluate it, you would press these keys: 3 ` 76 F D a 7 ` 9 \ - ˆ 5 E \ 2 < 45 b

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Chapter 1: Operating the TI-86

25

Using Functions in Expressions A function returns a value. Some examples of functions are ÷ , L , + , ‡ , and log. To use functions, you usually must enter one or more valid arguments. In this guidebook, optional arguments are shown in brackets ( ã and ä ). Do not include these brackets when you enter the arguments.

When this guidebook describes the syntax of a function or instruction, each argument is in italics. For example: sin angle. Press = to enter sin, and then enter a valid angle measurement (or an expression that resolves to angle). For functions or instructions with more than one argument, you must separate each argument from the other with a comma. Some functions require the arguments to be in parentheses. When you are unsure of the evaluation order, use parentheses to clarify a function’s place within an expression.

The A to Z Reference describes all TI-86 functions and instructions, including their required and optional arguments.

Using an Instruction An instruction initiates an action. For example, ClDrw is an instruction that, when executed, clears all drawn elements from a graph. You cannot use an instruction in an expression. Generally, the first letter of each instruction name is uppercase on the TI-86. Some instructions take more than one argument, as indicated by an open parenthesis ( ( ) at the end of the name. For example, Circl( requires three arguments, Circl(x,y,radius).

In the CATALOG, to move to the first item beginning with a letter, press that letter (as in ãLä in the example).

Entering Functions, Instructions, and Operators You can enter a function, instruction, or operator in any of three ways (log 45, for example). ♦ Paste it to the cursor location from the keyboard or a menu (< 45). ♦ Paste it to the cursor location from the CATALOG (- w & ãLä & & b 45). ♦ Enter it letter by letter ( - n 1 ãLä ãOä ãGä ¤ 1 1 45). As you can see in the example, using the built-in function or instruction typically is easier.

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26

Chapter 1: Operating the TI-86

When you select a function, instruction, or operator, a symbol comprising one or more characters is pasted to the cursor location. Once the symbol is pasted to the cursor location, you can edit individual characters. For example, assume that you pressed - w / / * & & b to paste yMin to the cursor location as part of an expression. Then you realized you wanted xMin. Instead of pressing nine keys to select xMin, you can simply press ! ! ! ! 2.

In the example, the ¶ symbol indicates that the value before it is to be stored to the variable after it (Chapter 2). To paste ¶ to the screen, press X.

Entering Consecutive Entries To enter two or more expressions or instructions consecutively, separate each from the next with a colon (- ). When you press b, the TI-86 executes each entry from left to right and displays the result of the last expression or instruction. The entire group entry is stored in last entry (page 28). The Busy Indicator When the TI-86 is calculating or graphing, a moving vertical line is displayed as the busy indicator in the top-right corner of the screen. When you pause a graph or a program, the busy indicator is replaced by the pause indicator, a moving vertical dotted line. Interrupting a Calculation or Graph To interrupt a calculation or graph in progress, press ^. When you interrupt a calculation, the ERROR 06 BREAK message and menu are displayed. ♦ To return to the home screen, select QUIT (press *). ♦ To go to the beginning of the expression, select GOTO (press &). Press b to recalculate the expression.

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Chapter 1: Operating the TI-86

Chapter 5: Function Graphing introduces graphing.

27

When you interrupt a graph, a partial graph and the GRAPH menu are displayed. ♦ To return to the home screen, press : : or any non-graphing key. ♦ To restart graphing, select an instruction that displays the graph.

Diagnosing an Error If a syntax error occurs within a stored equation during program execution, select GOTO to return to the equation editor, not to the program (Chapter 5).

When the TI-86 detects an error, it returns an error message, such as ERROR 04 DOMAIN or ERROR 07 SYNTAX. The Appendix describes each error type and possible reasons for the error. ♦ If you select QUIT (or press - l or : :), the home screen is displayed. ♦ If you select GOTO, the previous screen is displayed with the cursor on or near the error. Correcting an Error

Note the error type (ERROR ## errorType).



Select GOTO, if available. The previous screen is displayed with the cursor on or near the error.



Determine the cause for the error. If you cannot, refer to the Appendix for possible causes.



Correct the error and continue.

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28

Chapter 1: Operating the TI-86

Reusing Previous Entries and the Last Answer Retrieving the Last Entry When you press b on the home screen to evaluate an expression or to execute an instruction, the entire expression or instruction is placed in a storage area called ENTRY (last entry). When you turn off the TI-86, ENTRY is retained in memory. To retrieve the last entry, press - ¢. The current line is cleared and the entry is pasted to the line. Retrieving and Editing the Last Entry -¢



On the home screen, retrieve the previous entry.



Edit the retrieved entry.

! ! ! ! ! 32



Re-execute the edited entry.

b

Retrieving Previous Entries The TI-86 retains as many previous entries as possible in ENTRY, up to a capacity of 128 bytes. To scroll from the newest to the older previous entries stored to ENTRY, repeat - ¢. If you press - ¢ after displaying the oldest stored entry, the newest stored entry is displayed again; continuing to press - ¢ repeats the order.

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Chapter 1: Operating the TI-86

29

Consecutively entered entries separated by colons (page 26) are stored as one entry.

Retrieving Multiple Entries To store two or more expressions or instructions together to ENTRY, enter them on one line, separating each from the other with a colon, and then press b. Upon execution, the entire group is stored in ENTRY. The example below shows one of many ways you can manipulate this feature to avoid tedious manual re-entry.

The formula for finding the area of a circle is A=pr2.



The equation solver (Chapter 15) is another tool with which you can perform this task.



Use trial and error to find the radius of a circle with an area of 200 square centimeters. Store 8 to r as your first guess, then execute pr 2.

8 X - n ãRä - [:] - ~ ãRä 1

Retrieve 8¶r:pr 2 and insert 7.958 as a new guess. Continue guessing to approach the answer of 200.

-¢ - ! 7 - p ` 958 b

1Ib

Clearing the ENTRY Storage Area To clear all data from the ENTRY storage area, begin on a blank line on the home screen, select ClrEnt from the MEM menu (press - ™ *), and then press b. Retrieving the Last Answer When an expression is evaluated successfully on the home screen or in a program, the TI-86 stores the answer to a built-in variable called Ans (last answer). Ans may be a real or complex number, list, vector, matrix, or string. When you turn off the TI-86, the value in Ans is retained in memory.

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30

Chapter 1: Operating the TI-86

To copy the variable name Ans to the cursor location, press - ¡. You can use the variable Ans anywhere that the value stored to it is valid. When the expression is evaluated, the TI-86 calculates the result using the value stored in Ans. 1`7M4`2



Calculate the area of a garden plot 1.7 meters by 4.2 meters.



Calculate the yield per square meter if the plot 147 F - ¡ b produces a total of 147 tomatoes.

b

Using Ans Preceding a Function Previous answers are stored to Ans. If you begin an expression by entering a function that requires a preceding argument, the TI-86 automatically enters Ans as the argument.

Enter and execute an expression.

5F2b



Enter a function without an argument. Ans is pasted to the screen, followed by the function.

M9`9 b

Storing Results to a Variable

Calculate the area of a circle with radius 5 meters.

-~5I b



Calculate the volume of a cylinder of radius 5 meters and height 3.3 meters.

M3`3 b



Store the result to the variable V.

X ãVä b

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Chapter 1: Operating the TI-86

31

Using TI-86 Menus The symbols for many TI-86 features are found in menus instead of on the TI-86 keyboard. Displaying a Menu The way to display a particular menu depends on the menu’s location on the TI-86.

Some TI-86 menus have as many as 25 items.

Menu-Displaying Method

Example

Press a key that has a menu name on it

6 displays the GRAPH menu

Press - and then a 2nd-key menu name

- Πdisplays the MATH menu

Select a menu name from another menu

- Π& displays the MATH NUM menu

Select an editor or selection screen

- ” ) displays the list editor menu with the list editor

Accidentally commit an error

1 X b displays the error menu

When you display a menu, a menu group of one to five items is displayed on the bottom of the screen. If the more symbol ( 4 ) is displayed after the fifth item in a menu group, the menu continues for at least one more menu group. To view the next menu group, press /. The last menu group of one to five items does not have a 4 symbol. For example, press - Πto display the MATH menu.

", #, !, and $ do not work on menus.

When you see 4 here... ...press / to display the next menu group. From the last menu group, press / again to return to the first menu group.

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32

Chapter 1: Operating the TI-86

The Menu Keys

The Appendix Menu Map shows every TI-86 menu. Typically, a TI-86 menu item is five characters long or less.

- upper menu keys

M1

M2

M3

M4

M5

lower menu keys

&

'

(

)

*

- l clears all menus - e through i selects upper menu items

- ./

QUIT

/ scrolls lower menu groups . removes the lower menu

Selecting a Menu Item When you display a menu, one to five items are displayed. To select a menu item, press the menu selection key directly below the item. For example, in the MATH menu to the right, press & to select NUM, press ' to select PROB, and so on.

&

'

(

)

*

When you select a menu item that displays another menu, the first menu moves up one line on the screen to make room for the new menu. All items on the original menu are displayed in reverse type, except the item you selected. / only scrolls the lower menu; it does not scroll the upper menu.

When you select NUM... ...the MATH menu moves up and the MATH NUM menu is displayed. To remove the MATH NUM menu and move the MATH menu down, press ..

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Chapter 1: Operating the TI-86

33

To select an item from the upper menu, press - and the appropriate key e through i. To select PROB from the upper menu, press - f. To select iPart from the lower menu, press '.

When an editor menu is displayed as the upper menu, and you select an item from the lower menu that displays yet another menu, the editor menu remains as the upper menu. When you select NUM from the lower menu...

The MATH menu disappears.

...the equation editor menu remains and the MATH NUM menu is displayed. Upper: equation editor menu Lower: MATH NUM menu

Upper: equation editor menu Lower: MATH menu

To remove a menu from the bottom of a graph screen, press : after plotting the graph (Chapter 5).

Exiting (Removing) a Menu To remove the lower menu from the screen, press .. When you press ....

...the MATH NUM menu disappears and the MATH menu moves down.

Press . again, and the MATH menu disappears.

Upper: MATH menu Lower: MATH NUM menu

Lower: MATH menu

No menu

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Chapter 1: Operating the TI-86

Viewing and Changing Modes In the screen to the right, the default mode settings are highlighted along the left side of the screen.

To display the mode settings, press - m. The current settings are highlighted. Mode settings control how the TI-86 displays and interprets numbers and graphs. The Constant Memory feature retains current mode settings when the TI-86 is turned off. All numbers, including elements of matrices and lists, are displayed according to the mode settings. Changing a Mode Setting

This example changes the decimal mode setting to 2, as in U.S. dollars and cents.

In Normal notation, if the answer is more than 12 digits or the absolute value of the answer < .001, it is displayed in scientific notation. Notation modes do not affect how you enter numbers.



Move the cursor to the line of the setting that you want to change (decimal setting in the example).

#



Move the cursor to the setting you want (2 decimal places).

"""



Execute the change.

b

Notation Modes Normal

Displays results with digits to the left and right of the decimal (as in 123456.7)

Sci

(scientific) Displays results in two parts: significant digits (with one digit to the left of the decimal) are displayed to the left of E and the appropriate power of 10 is displayed to the right of E (as in 1.234567E5)

Eng

(engineering) Displays results in two parts: significant digits (with one, two, or three digits to the left of the decimal) are displayed to the left of E and the appropriate power of 10 (which is always a multiple of 3) is displayed to the right of E (as in 123.4567E3)

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Chapter 1: Operating the TI-86

35

Decimal Modes Float

(floating) Displays results up to 12 digits, plus any sign and the floating decimal point

(fixed)

(012345678901; each number is a setting) Displays results with the specified number of digits to the right of the decimal point (rounds answers to the specified decimal place); the second 0 sets 10; the second 1 sets 11

Angle Modes Radian

Interprets angle values as radians; displays answers in radians

Degree

Interprets angle values as degrees; displays answers in degrees

Complex Number Modes RectC

(rectangular complex mode) Displays complex-number results as (real,imaginary)

PolarC

(polar complex mode) Displays complex-number results as (magnitude±angle)

Graphing Modes Func

(function graphing) Plots functions where y is a function of x

Pol

(polar graphing) Plots functions where r is a function of q

Param

(parametric graphing) Plots relations where x and y are functions of t

DifEq

(differential equation graphing) Plots differential equations in terms of t

Number Base Modes Non-decimal modes are valid only on the home screen or in the program editor.

Dec

(decimal number base) Interprets and displays numbers as decimal (base 10)

Bin

(binary number base) Interprets numbers as binary (base 2); displays Ü suffix with answers

Oct

(octal number base) Interprets numbers as octal (base 8); displays Ý suffix with answers

Hex

(hexadecimal number base) Interprets numbers as hexadecimal (base 16); displays ß suffix with answers

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36

Chapter 1: Operating the TI-86

Vector Coordinate Modes Vector modes do not affect how you enter vectors.

RectV CylV SphereV

(rectangular vector coordinates) Displays answers in the form ãx yä for two-element vectors and ãx y zä for three-element vectors

(cylindrical vector coordinates) Displays results in the form ãr ±qä for two-element vectors and ãr ±q zä for three-element vectors (spherical vector coordinates) Displays results in the form ãr ± qä for two-element vectors and ãr ±q ±fä for three-element vectors

Differentiation Modes

The value stored to d affects

dxNDer (Appendix).

dxDer1

(exact differentiation) Uses der1 (Chapter 3) to differentiate exactly and calculate the value for each function in an expression (dxDer1 is more accurate than dxNDer, but it restricts the kinds of functions that are valid in the expression)

dxNDer

(numeric differentiation) Uses nDer to differentiate numerically and calculate the value for an expression (dxNDer is less accurate than dxDer1, but more kinds of functions are valid in the expression)

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2

The CATALOG, Variables, and Characters TI-86

The CATALOG .................................................................... 38 Storing Data to Variables................................................... 39 Classifying Variables as Data Types................................... 42 The CUSTOM Menu ........................................................... 44 The CHAR (Character) Menu.............................................. 45

M1

M2

M3

M4

M5

F1

F2

F3

F4

F5

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38

Chapter 2: The CATALOG, Variables, and Characters

The CATALOG The CATALOG is the first item on the CATLG-VARS menu.

-w&

The CATALOG displays all TI-86 functions and instructions in alphabetical order. Items that do not begin with a letter (such as + or 4Bin) are at the end of the CATALOG. The selection cursor ( 4 ) indicates the current item. To select an item from the CATALOG, move the selection cursor to the item and press b. The CATALOG disappears and the name is pasted to the previous cursor location.

Use # or $ to move 4 to an item...

...and press b. The item is pasted to the cursor location.

To jump...

Do this:

To the first item beginning with a particular letter

Press the letter; ALPHA-lock is on

To special characters at the end of the CATALOG

Press $ from the first CATALOG item

Down one whole screen

Select PAGE$ from the CATALOG menu ( & )

Up one whole screen

Select PAGE# from the CATALOG menu ( ' )

The menu items CUSTM and BLANK are on the CATALOG menu and each VARS screen menu. With them, you can create and edit your own CUSTOM menu of up to 15 CATALOG items and variables, including program names. For details about the CUSTOM menu, read page 44.

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Chapter 2: The CATALOG, Variables, and Characters

39

Storing Data to Variables This chapter describes the first two data storage methods listed here. The other methods are described in the appropriate chapters.

On the TI-86, data can be stored to variables in several ways. You can: ♦ Use X to store a value to a variable. ♦ Use = to store an unevaluated expression to an equation variable. ♦ Use an editor’s Name= prompt to store several types of data to a variable. ♦ Change TI-86 settings or reset defaults and memory to the factory settings. ♦ Execute functions that cause the TI-86 to store data automatically to built-in variables. The TI-86 has built-in variable names with specific purposes, such as equation variables, list names, statistical result variables, window variables, and Ans. You can store values to some of them. They are introduced in the appropriate chapters of this guidebook. Creating a Variable Name You can create your own variable name when you use X, =, or a Name= prompt to store data. When you create a user-created variable name, follow these guidelines. ♦ The user-created variable name can be from one to eight characters long. ♦ The first character must be a letter, which includes all CHAR GREEK menu items, as well as Ñ, ñ, Ç, and ç from the CHAR MISC menu. ♦ A user-created variable name cannot replicate a TI-86 feature symbol or built-in variable. For example, you cannot create abs, because abs is the absolute value function symbol. You cannot create Ans, because it is already a built-in variable name. ♦ The TI-86 distinguishes between uppercase and lowercase characters in variable names. For example, ANS, Ans, and ans are three different variable names. Therefore, only Ans is a built-in variable name; ANS and ans can be user-created variable names.

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40

Chapter 2: The CATALOG, Variables, and Characters

Storing a Value to a Variable Name

Enter a value, which can be an expression.

-~5I



Enter ¶ (the store symbol) next to the value.

X



Create a variable name one to eight characters long, starting with a letter. ALPHA-lock is on.

ãAä ãRä ãEä ãAä



Store the value to the variable. The value stored to the variable is displayed as a result.

b

Storing an Unevaluated Expression When you store an expression to memory using X (with the ¶ sign), the expression is evaluated and the result is stored to a variable. When you store an unevaluated expression using 1 ã=ä, or the equation editor (Chapter 5), or the equation solver (Chapter 15), the unevaluated expression is stored to an equation variable. When you use =, variable is first, then =, then expression. In contrast, when you use ¶, value is first, then ¶, then variable.

To store an unevaluated expression on the home screen or in a program, the syntax is: variable=expression where variable always precedes the equals sign and expression always follows the equals sign. You can use = to store a mathematical expression to an equation variable. For example, F=M¹A.

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Chapter 2: The CATALOG, Variables, and Characters

41

Storing an Answer To store an answer to a variable before you evaluate another expression, use X and Ans. In the example, the TI-86 multiplies the value stored to AREA times 3.3.



Enter and evaluate an expression.

11 ãAä ãRä ãEä ãAä 1 M3`3b

To paste AREA to the cursor location, you can press w (, move the selection cursor (4) to AREA, and press b.



Store the answer to a user-created variable or to a valid built-in variable. The value stored to the variable is displayed as a result.

X ãVä ãOä ãLä b

To paste ¶ to the cursor location, press X.

Copying a Variable Value To copy the contents of variableA into variableB, the syntax is: variableA¶variableB For example, RegEq¶y1 stores the regression equation (Chapter 14) to the variable y1. Displaying a Variable Value

To paste a variable name, you can select it from a VARS menu (page 42).



With the cursor on a blank line on the home screen, paste the variable name to the cursor location, as described above.

-w( # (location may vary) b



Display the contents of the variable.

b

You also can display variables containing some data types by displaying them in the appropriate editor (such as the list editor or window variable editor) or graph. These methods are detailed in subsequent chapters of this guidebook.

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42

Chapter 2: The CATALOG, Variables, and Characters

Recalling a Variable Value

To cancel RCL, press :.

Editing a recalled value does not change the value stored to the variable.



Move the cursor to where you want to insert the recalled variable value.

100 M



Display the Rcl prompt at the bottom of the screen. ALPHA-lock is on.

-–



Enter the variable name you want to recall.

[V] [O] [L]



Recall the variable contents to the cursor location. The Rcl prompt disappears and the entry cursor returns.

b

Classifying Variables as Data Types When you store data in an editor, the TI-86 recognizes the data type according to the editor. For example, only vectors are stored using the vector editor.

The TI-86 classifies variables according to data type and places each variable on a data-type selection screen. You can display each screen by selecting the appropriate data type from the CATLG-VARS menu, as described on page 43. Here are some examples. If data...

The TI-86 classifies the data type as...

For example:

Begins with { and ends with }

A list (VARS LIST screen)

{1,2,3}

Begins with ã and ends with ä

A vector (VARS VECTR screen)

ã1,2,3ä

Begins with ãã and ends with ää

A matrix (VARS MATRX screen)

ãã1,2,3äã4,5,6äã7,8,9ää

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Chapter 2: The CATALOG, Variables, and Characters

-w

The CATLG-VARS (CATALOG-Variables) Menu To display additional menu groups, press /.

The list names fStat, xStat, and yStat are statistical result variables on the VARS STAT screen.

CATLG

ALL

REAL

CPLX

LIST

43

4

VECTR MATRX STRNG

EQU

CONS

4

PRGM

STAT

WIND

GDB

PIC

CATLG

Displays the CATALOG

ALL

Displays a selection screen with all variables and names of all data types

REAL

Displays a selection screen with all real number variables

CPLX

Displays a selection screen with all complex number variables

LIST

Displays a selection screen with all list names

VECTR

Displays a selection screen with all vector names

MATRX

Displays a selection screen with all matrix names

STRNG

Displays a selection screen with all string variables

EQU

Displays a selection screen with all equation variables

CONS

Displays a selection screen with all user-defined constants

PRGM

Displays a selection screen with all program names

GDB

Displays a selection screen with all graph database names

PIC

Displays a selection screen with all picture names

STAT

Displays a selection screen with all statistical result variables

WIND

Displays a selection screen with all window variables

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44

Chapter 2: The CATALOG, Variables, and Characters

Selecting a Variable Name The example assumes that the real-number variables AREA and VOL from the example on page 41 have not been deleted from memory.



Select the appropriate data-type selection screen from the CATLG-VARS menu.

-w(



Move the cursor to the variable you want to select.

#



Select the variable you want.

b

The CUSTOM Menu

-w&(

You can select up to 15 items from the CATALOG and VARS screens -- program names, functions, instructions, and other items -- to create your own CUSTOM menu. To display your CUSTOM menu, press 9. Use & through * and / to select items like any other menu. Entering CUSTOM Menu Items

When copying items into the CUSTOM menu, you can skip



Select CUSTM from the CATALOG. The CUSTOM menu is displayed. ALPHA-lock is on.

-w &(



Move the selection cursor ( 4 ) to the item you want to copy to the CUSTOM menu.

ãCä # # #



Copy the item to the CUSTOM menu cell you select, replacing any previous item.

(



To enter more items, repeat steps 2 and 3 using different items and cells.



Display the CUSTOM menu.

menu cells and menu groups.

-l 9

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Chapter 2: The CATALOG, Variables, and Characters

45

Clearing CUSTOM Menu Items To clear an item from the second or third menu group, press / until the item is displayed, and then select it.

You cannot delete a TI-86 built-in variable. You cannot delete a program variable using DelVar( .



Select BLANK from the CATALOG menu. The CUSTOM BLANK menu is displayed.

-w &)



Clear the menu item.

(



To clear more items, repeat steps 2 and 3.

Deleting a Variable from Memory From the home screen or in a program, to delete from memory one user-created variable name (except a program name) and its contents, the syntax is: DelVar(variable) To delete user-created variable names and their contents (including program names), display the MEM DELET menu (- ™ '), select the data type, select the variable, and then press b (Chapter 16). Deleting a variable does not remove it from the CUSTOM menu (page 44).

The CHAR (Character) Menu MISC

GREEK



INTL

miscellaneous international characters characters menu menu Greek characters menu

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46

Chapter 2: The CATALOG, Variables, and Characters

-Ÿ&

The CHAR MISC (Miscellaneous) Menu Ñ, ñ, Ç, and ç are valid as

any character of a variable name, including the first letter.

MISC ?

GREEK #

INTL &

%

'

4

!

@

$

~

|

4

¿

Ñ

ñ

Ç

ç

4

H

q

l

m

r

4

G

s

τ

f

J

%, ' , and ! can be functions.

The CHAR GREEK Menu All CHAR GREEK menu items are valid variable-name characters, including the first letter. p ( - ~ ) is not valid as a character; p is a constant on the TI-86.

MISC a

GREEK b

INTL g

-Ÿ' @

The CHAR INTL (International) Menu MISC ´

GREEK `

INTL ^

d

-Ÿ(

¨

You can combine modifiers on the CHAR INTL menu with uppercase or lowercase vowels to create vowels used in some languages. You can use these vowels in variable names and text. Adding a Modifier to a Vowel

Select the modifier from the CHAR INTL menu. ALPHA-lock is on. If necessary, switch to alpha-lock.

-Ÿ() -n



Enter the uppercase or lowercase vowel over which you want the modifier.

ã Oä

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3

Math, Calculus, and Test Operations TI-86

Keyboard Mathematical Functions .................................... 48 The MATH Menu................................................................ 49 The CALC (Calculus) Menu ................................................ 54 The TEST (Relational) Menu............................................... 55

M1

M2

M3

M4

M5

F1

F2

F3

F4

F5

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48

Chapter 3: Math, Calculus, and Test Operations

Keyboard Mathematical Functions The A to Z Reference details which data types are valid arguments for each function.

You can use these mathematical functions in expressions with real or complex values. You can use some of them with lists, vectors, matrices, or strings. When you use lists, vectors, or matrices, the valid functions return a list of results calculated on an element-by-element basis. If you use two lists, vectors, or matrices in the same expression, they must be equal in dimension.

The most common mathematical functions are on the TI-86 keyboard. For syntax, details, and examples of these functions, refer to the A to Z Reference.

x -1 (the multiplicative inverse) is equivalent to the reciprocal, 1àx.

Key

Function

Key

Function

\ T M F a I -ˆ -ƒ @ -z

+ (add)

= > ? -{ -| -} < B -‚ -~

sin (sine)

C

E (exponent)

N (subtract) ¹ (multiply) à (divide) M (negate) 2

(square) ‡ (square root) L1 (inverse) ^ (raise to a specified power) 10^ (10 to a specified power)

cos (cosine) tan (tangent) sinL1 (arcsine; inverse of sine) cosL1 (arccosine; inverse of cosine) tanL1 (arctangent; inverse of tangent) log (logarithm) ln (natural log) ex (constant e raised to a power) p (constant pi; 3.1415926535898)

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Chapter 3: Math, Calculus, and Test Operations

The MATH Menu NUM

PROB

number menu

ANGLE angle menu

probability menu

-ΠHYP

value can sometimes be an expression, list, vector, or matrix. For details about specific syntax options and examples, refer to the A to Z Reference.

PROB iPart

ANGLE fPart

round(value[,#ofDecimals]) iPart value fPart value int value abs value sign value min(valueA,valueB) min(list) max(valueA,valueB) max(list) mod(numberA,numberB)

4

INTER

miscellaneous math functions menu hyperbolic interpolate menu editor

The MATH NUM (Number) Menu NUM round

MISC

HYP int

-Œ& MISC abs

4

sign

min

max

mod

Rounds value to 12 decimal places or to #ofDecimals Returns the integer part or parts of value Returns the fractional part or parts of value Returns the largest integer less than or equal to value Returns the absolute value or magnitude of value Returns 1 if value is positive; 0 if value is 0; L1 if value is negative Returns the smaller of valueA and valueB Returns the smallest element of list Returns the larger of valueA and valueB Returns the largest element of list Returns numberA modulo numberB

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49

50

Chapter 3: Math, Calculus, and Test Operations

The MATH PROB (Probability) Menu NUM ! ! (factorial) is valid for nonintegers.

randInt, randNorm, and randBin are abbreviated in the MATH PROB menu.

PROB nPr

ANGLE nCr

HYP rand

-Œ' MISC randIn

4

randN

randBi

value!

Returns the factorial of a real value

items nPr number

Returns the number of permutations of items (n) taken number (r) at a time

items nCr number

Returns the number of combinations of items (n) taken number (r) at a time

rand

Returns a random number > 0 and < 1; to control a random number sequence, first store an integer seed value to rand (such as 0¶rand)

randInt(lower,upper ã,#ofTrialsä )

(random integer) Returns a random integer bound by the specified integers, lower  integer  upper; to return a list of random integers, specify an integer > 1 for #ofTrials

randNorm(mean,

(random normal) Returns a random real number from a normal distribution specified by mean and stdDeviation; to return a list of random numbers, specify an integer > 1 for #ofTrials

stdDeviation ã,#ofTrialsä ) randBin(#ofTrials,

probabilityOfSuccess ã,#ofSimulationsä )

(random binomial) Returns a random real number from a binomial distribution, where #ofTrials ‚ 1 and 0  probabilityOfSuccess  1; to return a list of random numbers, specify an integer > 1 for #ofSimulations

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Chapter 3: Math, Calculus, and Test Operations

The MATH ANGLE Menu NUM o angle can be a list for ¡ , r , and 4DMS.

In a calculation, the result of a degrees'minutes'seconds' entry is treated as degrees in Degree angle mode only. It is treated as radians in Radian angle mode.

ANGLE '

-Œ( HYP 4DMS

MISC

angle¡

Overrides current angle mode setting to express angle in degrees

angler

Overrides current angle mode setting to express angle in radians

degrees'minutes'seconds'

Designates an angle as degrees, minutes, and seconds

angle4DMS

Displays angle in degrees¡minutes'seconds" format, even though you use degrees'minutes'seconds' to enter a DMS angle

The MATH HYP (Hyperbolic) Menu NUM sinh

value can sometimes be an expression, list, vector, or matrix. For details about specific syntax options and examples, refer to the A to Z Reference.

PROB r

51

PROB cosh

sinh value cosh value tanh value sinhL1 value coshL1 value tanhL1 value

ANGLE tanh

HYP sinh- 1

-Œ) MISC cosh- 1

4

tanh- 1

Returns the hyperbolic sine of value Returns the hyperbolic cosine of value Returns the hyperbolic tangent of value Returns the hyperbolic arcsine of value Returns the hyperbolic arccosine of value Returns the hyperbolic arctangent of value

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Chapter 3: Math, Calculus, and Test Operations

The MATH MISC (Miscellaneous) Menu NUM sum value can sometimes be an expression, list, vector, or matrix. For details about specific syntax options, refer to the A to Z Reference.

PROB prod

ANGLE seq

HYP lcm

-Œ*

MISC gcd

4

4Frac

%

pEval

x



eval

sum list

Returns the sum of the elements of list

prod list

Returns the product of the elements of list

seq(expression,variable, begin,end[,step])

Returns a list in which each element is the value of expression evaluated for variable from begin to end by step

lcm(valueA,valueB)

Returns the least common multiple of valueA and valueB

gcd(valueA,valueB)

Returns the greatest common divisor of valueA and valueB

value4Frac

Displays value as a fraction

value%

Returns value divided by 100 (multiplied by .01)

percent%number

Returns percent of number

pEval(coefficientList,xValue)

Returns the value of a polynomial (whose coefficients are given in coefficientList) at xValue

x throotx‡value

Returns the x throot of value

eval value

Returns a list of the values of all selected functions in the current graphing mode for the real value of the independent variable

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Chapter 3: Math, Calculus, and Test Operations

53

The InterpolateàExtrapolate Editor - Œ / & Using the interpolateàextrapolate editor, you can interpolate or extrapolate a value linearly, given two known pairs and the x-value or y-value of the unknown pair. To interpolate y from the home screen, select inter( from the CATALOG, and then enter inter(x1,y1,x2,y2,x).



Display the interpolateàextrapolate editor.

-Œ/&



Enter real values for the first known pair (x1,y1). The values can be expressions.

3b5b

To interpolate x from the home screen, enter inter(y1,x1,y2,x2,y).



Enter values for the second known pair (x2,y2).

4b4b



Enter a value for either the x value or the y value of the unknown pair.

1b



If necessary, move the cursor to the value for which you want to solve (x or y).

$ or #



Select SOLVE.

*

You can store individual values with the X key (Chapter 2).

The result is interpolated or extrapolated and displayed; the variables x and y are not changed. A solid square in the first column indicates the interpolated or extrapolated value. After solving for a value, you can continue to use the interpolateàextrapolate editor.

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Chapter 3: Math, Calculus, and Test Operations

The CALC (Calculus) Menu You must set Dec mode to use the calculus functions.

evalF

nDer

der1

der2

fnInt

-† 4

fMin

fMax

arc

The calculus functions return values with respect to any user-created variable, to built-in variables eqn and exp, and to graphing variables such as x, t, and q. evalF(expression,variable,value) For evalF, nDer, der1, and der2, variable can be a real

nDer(expression,variable ã,valueä) Returns an approximate numerical derivative of expression with

respect to variable for the current variable value or specified variable value

or complex number or list. You can use der1 and der2 in expression. You can use nDer once in expression.

Returns the value of expression with respect to variable for a given variable value

der1(expression,variableã,valueä) Returns the value of the first derivative of expression with respect to

variable for the current variable value or specified variable value der2(expression,variableã,valueä) Returns the value of the second derivative of expression with respect

to variable for the current variable value or specified variable value For fnInt, fMin, and fMax, lower < upper must be true.

fnInt(expression,variable, lower,upper)

Returns the numerical integral of expression with respect to variable between lower and upper boundaries

fMin(expression,variable, lower,upper)

Returns the minimum value of expression with respect to variable between lower and upper boundaries

fMax(expression,variable, lower,upper)

Returns the maximum value of expression with respect to variable between lower and upper boundaries

arc(expression,variable, start,end)

Returns the length of a segment of a curve defined by expression with respect to variable between start and end

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Chapter 3: Math, Calculus, and Test Operations

55

The built-in variable d defines the step size in calculating nDer( (in dxNDer differentiation mode only) and arc(. The built-in variable tol defines the tolerance in calculating fnInt(, fMin(, fMax(, and arc(. The value of each must be >0. These factors affect the accuracy of the calculations. As d becomes smaller, the approximation typically is more accurate. For example, nDer(A^3,A,5) returns 75.0001 if d=.01, but returns 75 if d=.0001 (Appendix). The function integral error value is stored to the variable fnIntErr (Appendix). For arc( and fnInt( while dxDer1 mode is set, these functions are not valid in expression: evalF(, der1(, der2(, fMin(, fMax(, nDer(, seq(, and any equation variable, such as y1. You can approximate the fourth derivative at the current value of x with this formula: nDer(nDer(der2(x^4,x),x),x).

The TEST (Relational) Menu == Relational functions are valid for two lists of the same length. When valueA and valueB are lists, a list of results calculated element by element is returned.

<

>





-˜ 4

ƒ

valueA==valueB (equal to) Returns 1 if valueA is equal to valueB; returns 0 if not equal; valueA and valueB can be real or complex numbers, lists, vectors, matrices, or strings valueA
(less than) Returns 1 if valueA is less than valueB; returns 0 if valueA is not less than valueB; valueA and valueB must be real numbers or lists

valueA>valueB

(greater than) Returns 1 if valueA is greater than valueB; returns 0 if valueA is not greater than valueB; valueA and valueB must be real numbers or lists

valueA  valueB (less than or equal to) Returns 1 if valueA is less than or equal to valueB; returns 0 if valueA is not less than or equal to valueB; valueA and valueB must be real numbers or lists

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Chapter 3: Math, Calculus, and Test Operations

You can use relational functions to control program flow (Chapter 16).

valueA‚valueB

(greater than or equal to) Returns 1 if valueA is greater than or equal to valueB; returns 0 if valueA is not greater than or equal to valueB; valueA and valueB must be real numbers or lists

valueAƒvalueB

(not equal to) Returns 1 if valueA is not equal to valueB; returns 0 if valueA is equal to valueB; valueA and valueB can be real or complex numbers, lists, vectors, matrices, or strings

Using Tests in Expressions and Instructions The TI-86 Evaluation Operating System (Appendix) performs all operations except Boolean operators before it performs relational functions. For example: ♦ The expression 2+2==2+3 evaluates to 0. The TI-86 performs the addition first, and then compares 4 to 5. ♦ The expression 2+(2==2)+3 evaluates to 6. The TI-86 performs the test in parentheses first, and then adds 2, 1, and 3.

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4

Constants, Conversions, Bases, and Complex Numbers TI-86

Using Built-In and User-Created Constants ....................... 58 Converting Units of Measure ............................................. 61 Number Bases.................................................................... 65 Using Complex Numbers ................................................... 70

M1

M2

M3

M4

M5

F1

F2

F3

F4

F5

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Chapter 4: Constants, Conversions, Bases, and Complex Numbers

Using Built-In and User-Created Constants A constant is a variable with a specific value stored to it. The CONS BLTIN menu items are common constants built into the TI-86. You cannot edit the value of a built-in constant. You can create your own constants and add them to the user-created constant menu for easy access. To enter a user-created constant, you must use the user-created constant editor (page 60); you cannot use X or = to create a constant. -‘

The CONS (Constants) Menu BLTIN

EDIT

USER

built-in user-created constants menu constants menu user-created constants editor

The CONS BLTIN (Built-In Constants) Menu You can select built-in constants from the CONS BLTIN menu or enter them using the keyboard and the CHAR GREEK menu.

BLTIN Na

EDIT k

USER Cc

ec

Rc

-‘& 4

Gc

g

Me

Mp

Mn

4

m0

H0

h

c

u

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Chapter 4: Constants, Conversions, Bases, and Complex Numbers

To use p, press - ~ or select it from the CATALOG. To use e^, press - ‚. To use e, press - n ãEä.

Built-In Constant

Constant Name

Constant Value

Na

Avogadro's number

6.0221367E23 mole L1

k

Boltzman's constant

1.380658EL23 JàK

Cc

Coulomb constant

8.9875517873682E9 N m 2àC 2

ec

Electron charge

1.60217733EL19 C

Rc

Gas constant

8.31451 Jàmole K

Gc

Gravitational constant

6.67259EL11 N m 2àkg 2

g

Earth acceleration due to gravity

9.80665 màsec 2

Me

Mass of an electron

9.1093897EL31 kg

Mp

Mass of a proton

1.6726231EL27 kg

Mn

Mass of a neutron

1.6749286EL27 kg

m0

Permeability of a vacuum

1.2566370614359EL6 NàA 2

H0

Permittivity of a vacuum

8.8541878176204EL12 Fàm

h

Planck's constant

6.6260755EL34 J sec

c

Speed of light in a vacuum

299,792,458 màsec

u

Atomic mass unit

1.6605402EL27 kg

p

Pi

3.1415926535898

e

Base of natural log

2.718281828459

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60

Chapter 4: Constants, Conversions, Bases, and Complex Numbers

Creating or Redefining a User-Created Constant CONS USER menu items are



Display the CONS menu.

-‘



Display the constant editor. The Name= prompt, Value= prompt, and CONS USER menu are displayed. ALPHA-lock is on.

'

196.9665 is the atomic weight of gold (Au).



Enter a constant name. Either enter a new name one to eight characters long, starting with a letter, or select a name from the CONS USER menu. The cursor moves to the Value= prompt and the CONS EDIT menu is displayed (see below).

ãAä - n ãUä b

You can enter a value later.



Enter the real or complex constant value, which can be an expression. The value is stored to the constant as you enter it. The user-created constant becomes a CONS USER menu item.

196 ` 9665

the names of all stored usercreated constants, arranged alphanumerically.

If you select PREV when the first constant name is displayed, or NEXT when the last constant name is displayed, the CONS USER menu replaces the CONS EDIT menu. You also can delete a constant from the MEM DELET CONS screen.

The Constant Editor Menu PREV

NEXT

- ‘ ' name b or #

DELET

PREV

Displays the name and value (if any) of the previous constant on the CONS USER menu

NEXT

Displays the name and value (if any) of the next constant on the CONS USER menu

DELET Deletes the name and value of the constant currently displayed in the constant editor

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Chapter 4: Constants, Conversions, Bases, and Complex Numbers

61

Entering a Constant Name in an Expression You can enter a constant in an expression in any of three ways. ♦ Select the constant name from the CONS BLTIN menu or the CONS USER menu. ♦ Select a user-created constant name from the VARS CONS screen. ♦ Use the ALPHA keys, alpha keys, and other character keys to enter a constant name.

Converting Units of Measure You can enter a conversion expression anywhere that an expression is valid.

With the TI-86, you can convert a value measured in one unit into its equivalent value in another unit of measure. For example, you can convert inches to yards, quarts to liters, or degrees Fahrenheit to degrees Celsius. The units of measure from which and to which you convert must be compatible. For example, you cannot convert inches to degrees Fahrenheit, or yards to calories. Each menu item on the CONV menu (page 62) represents a unit-of-measure group, such as length (LNGTH), volume (VOL), and pressure (PRESS). Within each menu, all units are compatible. Converting a Unit of Measure To use any conversion instruction, the syntax is: (value)currentUnit4newUnit

In the example, L2 degrees Celsius is converted to degrees Fahrenheit. Always use parentheses when value is negative.



Enter the real value to be converted.

Da2E



Display the CONV menu.

-’



Select the TEMP conversion group.

*

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62

Chapter 4: Constants, Conversions, Bases, and Complex Numbers Select the current unit of measure (¡C) from the conversion group menu. The unit abbreviation and conversion symbol ( 4 ) are pasted to the cursor location.

&

Select the new unit of measure (¡F) from the conversion group menu. The unit abbreviation is pasted to the cursor location.

'



b

Convert the measurement.

The CONV (Conversions) Menu LNGTH

AREA

VOL

length menu

volume menu area menu

TIME

-’ TEMP

4

MASS

4

SPEED

temperature speed menu menu time menu mass menu

FORCE PRESS ENRGY POWER

force menu

energy menu pressure menu power menu

Important: When you convert a negative value, you must enclose in parentheses the value and its negation sign, as in (L4). Otherwise, the TI-86 order of evaluation will perform the conversion first, and then apply the negation to the converted value. If you enter...

...The TI-86 converts it to...

(L4)¡C4¡F

24.8 degrees Fahrenheit (L4¡ Celsius converted to degrees Fahrenheit)

L4¡C4¡F

L39.2 degrees Fahrenheit (4¡ Celsius converted to degrees Fahrenheit, then negated)

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Chapter 4: Constants, Conversions, Bases, and Complex Numbers

-’&

The CONV LNGTH (Length) Menu mm cm m in ft

millimeters centimeters meters inches feet

yd km mile nmile lt-yr

The CONV AREA Menu ft 2 m2 mi 2

The CONV VOL (Volume) Menu liter gal qt pt oz

square kilometers acres square inches

seconds minutes hours

cubic centimeters cubic inches cubic feet cubic meters cups

day yr week

days years weeks

The CONV TEMP (Temperature) Menu ¡C degrees Celsius

cm 2 yd 2 ha

square centimeters square yards hectares

tsp tbsp ml galUK ozUk

teaspoons tablespoons milliliters UK gallons UK ounces

ms ms ns

milliseconds microseconds nanoseconds

-’)

The CONV TIME Menu sec mn hr

mils Angstroms fermis rods fathoms

-’(

cm3 in3 ft3 m3 cup

liters gallons quarts pints ounces

mil Ang fermi rod fath

-’' km 2 acre in 2

square feet square meters square miles

yards kilometers miles nautical miles light-years

¡F

-’*

degrees Fahrenheit

¡K degrees Kelvin

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¡R degrees Rankin

63

64

Chapter 4: Constants, Conversions, Bases, and Complex Numbers

The CONV MASS Menu gm kg lb

grams kilograms pounds

The CONV FORCE Menu N dyne

Newtons dynes

-’/& atomic mass units slugs

amu slug

ton force kilogram force

tonf kgf

atm lbàin pounds per square inch atmospheres bar mmHg millimeters of mercury bars Nàm2 Newtons per square meter mmH2 millimeters of water

The CONV ENRGY (Energy) Menu

The CONV POWER Menu hp W

horsepower Watts

The CONV SPEED Menu ftàs màs

feet per second meters per second

lbf

pound force

-’/( 2

Joules calories British thermal units

tons metric tons

-’/'

The CONV PRESS (Pressure) Menu

J cal Btu

ton mton

inHg inches of mercury inH2O inches of water

-’/)

ft-lb foot-pounds kw-hr kilowatt hours eV electron Volts

erg l-atm

ergs liter-atmospheres

-’/* ftlbàs calàs

foot-pounds per second calories per second

Btuàm British thermal units

per minute

-’//& miàhr miles per hour kmàhr kilometers per hour

knot

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knots

Chapter 4: Constants, Conversions, Bases, and Complex Numbers

To enter a forward slash ( à ), you can use the F key or paste it from the CATALOG.

65

Converting a Value Expressed as a Rate To convert a value expressed as a rate on the home screen, you can use parentheses and the division operator ( à ). For example, if a car travels 325 miles in 4 hours, and you want to know the rate of speed in kilometers per hour, enter this expression: (325à4)miàhr4kmàhr This expression returns 131 kmàhr (rounded up). You also can return this result using only a forward slash, as in: 325mile4kmà4hr4hr

Number Bases The number base mode setting (Chapter 1) controls how the TI-86 interprets an entered number and displays results on the home screen. However, you can enter numbers in any number base using number base designators Ü, Ý, Þ, and ß. Then you can display the result on the home screen in any number base using number base conversions. All numbers are stored internally as decimal. If you perform an operation in a mode setting other than Dec, the TI-86 performs integer mathematics, truncating to an integer after every calculation and expression. For example, in Hex mode, 1à3+7 returns 7h (1 divided by 3, truncated to 0, and then added to 7).

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Chapter 4: Constants, Conversions, Bases, and Complex Numbers

Number Base Ranges Binary, octal, and hexadecimal numbers on the TI-86 are defined in these ranges. Type

Low ValueàHigh Value

Decimal Equivalent

Binary

1000 0000 0000 0001b 0111 1111 1111 1111b 5120 6357 4134 0001o 2657 1420 3643 7777o ÚÚÚÚ Õ50× ÙÚ85 ×001h 0000 5ÕÚ3 107Õ 3ÚÚÚh

L32,767

Octal Hexadecimal

32,767 L99,999,999,999,999

99,999,999,999,999 L99,999,999,999,999

99,999,999,999,999

One’s and Two’s Complements To obtain the one's complement of a binary number, enter the not function (page 68) before the number. For example, not 111100001111 in Bin mode returns 1111000011110000Ü. To obtain the two's complement of a binary number, press a before entering the number. For example, L111100001111 in Bin mode returns 1111000011110001Ü. The (Number) BASE Menu Õ-Ú

TYPE

CONV

-— BOOL

BIT

hexadecimal base conversion rotateàshift characters menu menu menu base type Boolean operator menu menu

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67

Chapter 4: Constants, Conversions, Bases, and Complex Numbers BASE Õ-Ú menu items and BASE TYPE menu items are

not the same as regular alphabetical characters.

In the example, the upper menu is the list editor menu ( - ” in Dec number base mode).

If Hex number base mode is not set, you must enter the ß designator, even if the number contains a special hexadecimal character.

The BASE Õ-Ú (Hexadecimal Characters) Menu

-—&

This is the BASE Õ-Ú menu displayed on the home screen. To use Õ, press - e.

Õ Ö

TYPE ×

CONV Ø

BOOL Ù

BIT Ú ...Õ and Ö move to two separate cells, and Ù and Ú are combined. To switch back, press * or /.

When an editor menu is the upper menu, Õ and Ö are combined in one cell. If you press & or /...

{ Õ-Ö

} ×

NAMES Ø

" Ù

OPS Ú

4

{ Õ

} Ö

NAMES ×

" Ø

OPS Ù-Ú

Entering Hexadecimal Digits To enter a hexadecimal number, use the number keys as you would for a decimal number. Select the hexadecimal characters Õ through Ú from the menu as needed. The BASE TYPE Menu Õ-Ú Ü

TYPE ß

-—'

CONV Ý

BOOL Þ

BIT

In an expression, you can designate a number in any number base, regardless of mode. After you enter the number, select the appropriate base type symbol from the BASE TYPE menu. The base type symbol is pasted to the cursor location. Here are some examples. In Dec mode (default):

10Ü+10 b 10ß+10 b

In Bin mode:

10ß+10 b 10Þ+10 b

10Ü+10 b 10Þ+10 b

12Ý 22Ý

10010Ü In Hex mode: 10Ü+10 b 10Þ+10 b 1100Ü

12ß 1Õß

12 In Oct mode: 26

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Chapter 4: Constants, Conversions, Bases, and Complex Numbers

The BASE CONV (Conversion) Menu Õ-Ú 4Bin value can be an expression, list, vector, or matrix. For detailed syntax descriptions, refer to the A to Z Reference.

value4Bin value4Hex

TYPE 4Hex

CONV 4Oct

BOOL 4Dec

-—( BIT

Displays value as binary Displays value as hexadecimal

value4Oct value4Dec

Displays value as octal Displays value as decimal

Converting Number Bases In Dec mode, solve 10Ü + Úß + 10Ý + 10.

10Ü+Úß+10Ý+10 b



Add 1 to the result and convert it to Bin number base display.

Ans+14Bin b

100100Ü



Add 1 to the result and convert it to Hex number base display.

Ans+14Hex b

25ß



Add 1 to the result and convert it to Oct number base display.

Ans+14Oct b

46Ý



Add 1 to the result and convert it to Dec number base display.

Ans+1 b



The BASE BOOL (Boolean) Menu Õ-Ú and

TYPE or

valueA and valueB

CONV xor

BOOL not

-—) BIT

valueA or valueB

valueA xor valueB

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not value

35

39

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Chapter 4: Constants, Conversions, Bases, and Complex Numbers

Both the argument and the result must be within defined number ranges (page 66).

Results of Boolean Operations When a Boolean expression is evaluated, the arguments are converted to hexadecimal integers and the corresponding bits of the arguments are compared, as this table shows. Results If valueA is... ...and valueB is... 1 1 0 0

and

or

xor

not (valueA)

1 0 0 0

1 1 1 0

0 1 1 0

0 0 1 1

1 0 1 0

The result is displayed according to the current mode setting. For example: ♦ In Hex mode, 5 and 6 returns 4ß. ♦ In Bin mode, 101 and 110 returns 100Ü. The BASE BIT Menu Rotate and shift operate on 16 base digits. To minimize an overflow error, enter the argument in binary form.

Õ-Ú rotR rotR value rotL value shftR value shftL value

TYPE rotL

-—*

CONV shftR

BOOL shftL

BIT

Rotates value right Rotates value left Shifts value right Shifts value left

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Chapter 4: Constants, Conversions, Bases, and Complex Numbers

Using Complex Numbers Variable names with complex numbers stored to them are listed on the VARS CPLX screen (Chapter 2). Lists, matrices, and vectors can have complex elements.

A complex number has two components: real (a) and imaginary (+bi). On the TI-86, you enter the complex number a+bi as: ♦ (magnitude±angle) in polar form ♦ (real,imaginary) in rectangular form You can enter a complex number in rectangular or polar form, regardless of the current complex number mode setting. The separator ( , or ± ) determines the form. ♦ To enter rectangular form, separate real and imaginary with a comma (P). ♦ To enter polar form, separate magnitude and angle with an angle symbol (- ). Each component (real, imaginary, magnitude, or angle) can be a real number or an expression that evaluates to a real number; expressions are evaluated when you press b. When RectC complex number mode is set, complex numbers are displayed in rectangular form, regardless of the form in which you enter them (as shown to the right). When PolarC complex number mode is set, complex numbers are displayed in polar form, regardless of the form in which you enter them (as shown to the right).

The graph format settings RectGC and PolarGC

(Chapter 5) determine the complex number form of graph screen coordinates.

Complex Results Complex numbers in results, including list, matrix, and vector elements, are displayed in the form (rectangular or polar) specified by the mode setting (Chapter 1) or by a display conversion instruction (page 61). ♦ When Radian angle mode is set, results are displayed as (magnitude±angle). ♦ When Degree angle mode is set, results are displayed as (real,imaginary).

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Chapter 4: Constants, Conversions, Bases, and Complex Numbers

71

For example, when PolarC and Degree modes are set, (2,1)N(1±45) returns (1.32565429614±12.7643896828). Using a Complex Number in an Expression ♦ Enter the complex number directly. ♦ Use the ALPHA keys, alpha keys, and other character keys to enter a complex variable. ♦ Select a complex variable from the VARS CPLX screen. The CPLX (Complex Number) Menu conj You can enter the name or a complex list, vector, or matrix as an argument for any CPLX menu item.

real

imag

abs

-‹ angle

4

4Rec

4Pol

conj (real,imaginary)

Returns the complex conjugate of a complex value, list, vector or matrix; the result is (real,Limaginary)

conj (magnitude±angle)

Returns (magnitude±Langle)

real (real,imaginary)

Returns the real portion of a complex number, list, vector, or matrix as a real number; the result is real

real (magnitude±angle)

Returns magnitude¹cosine(angle)

imag (real,imaginary)

Returns the imaginary (non-real) portion of a complex number, list, vector, or matrix as a real number; the result is imaginary

imag (magnitude±angle)

Returns magnitude¹sine(angle)

abs (real,imaginary)

(Absolute value) Returns the magnitude (modulus) of a complex number, list, vector, or matrix of complex numbers; the result is ‡(real 2+imaginary 2)

abs (magnitude±angle)

Returns magnitude

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Chapter 4: Constants, Conversions, Bases, and Complex Numbers

Select { and } from the LIST menu. You must enter commas to separate list elements.

angle (real,imaginary)

Returns the polar angle of a complex number, list, vector, or matrix calculated as tanL1 (imaginaryàreal) (adjusted by p in the second quadrant or Lp in the third quadrant); the result is tanL1(imaginaryàreal)

angle (magnitude±angle)

Returns angle (where Lp
complexValue4Rec

Displays complexValue in rectangular format (real,imaginary), regardless of complex mode setting; valid only at the end of a command and only when complexValue is indeed complex

complexValue 4Pol

Displays complexValue in polar format (magnitude±angle), regardless of complex mode setting; valid only at the end of a command and only when complexValue is indeed complex

You can enter a complex list, vector, or matrix directly. The syntax below is for lists. To enter a complex vector or matrix, substitute brackets for braces below and use the correct form for either data type (Chapters 12 and 13). In rectangular form, to use lists of complex numbers with conj, real, imag, abs, and angle, the syntax is: conj{(realA,imaginaryA),(realB,imaginaryB),(realC,imaginaryC),...} In polar form, to use lists of complex numbers with conj, real, imag, abs, and angle, the syntax is: real{(magnitudeA±angleA),(magnitudeB±angleB),(magnitudeC±angleC),...} When you use a list the TI-86 calculates the result element by element and returns a list, in which each element is expressed according to the complex mode setting.

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5

Function Graphing TI-86

Defining a Graph................................................................ 74 Setting the Graph Mode .................................................... 74 The GRAPH Menu .............................................................. 75 Using the Equation Editor .................................................. 76 Setting the Window Variables ........................................... 81 Setting the Graph Format .................................................. 83 Displaying a Graph ............................................................ 85 M1

M2

M3

M4

M5

F1

F2

F3

F4

F5

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74

Chapter 5: Function Graphing

Defining a Graph This chapter describes the process for graphing functions in Func graphing mode, but the process is similar for each TI-86 graphing mode. Chapters 8, 9, and 10 describe the unique aspects of polar, parametric, and differential equation graphing modes. Chapter 6 describes various graphing tools, many of which you can use in all graphing modes. Some of these steps are not necessary every time you define a graph.



Set the graphing mode (page 74).



Define, edit, or select one or more functions in the equation editor (pages 76 and 77).



Select the graph style for each function (page 79).



Deselect stat plots, if necessary (page 81).



Set the viewing window variables (page 81).



Select the graph format settings (page 83).

Setting the Graph Mode To display the mode screen, press - m. All default mode settings, including Func graphing mode, are highlighted in the picture to the right. The graphing modes are on the fifth line. ♦ Func (function graphing) ♦ Pol (polar graphing; Chapter 8) ♦ Param (parametric graphing; Chapter 9) ♦ DifEq (differential equation graphing; Chapter 10)

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Chapter 5: Function Graphing

75

Each graphing mode has a unique equation editor. You must select the graphing mode and Dec number base mode before you enter the functions. The TI-86 retains in memory all equations stored to the Func, Pol, Param, and DifEq equation editors. Each mode also has unique graph format settings and window variables. Stat plot onàoff status, zoom factors, mode settings, and tolerance apply to all graphing modes; changing the graphing mode does not affect them. Chapter 1 describes all mode settings in detail.

These mode settings affect graphing results. ♦ ♦

Radian or Degree angle mode affects the interpretation of some functions. dxDer1 or dxNDer differentiation mode affects plotting of selected functions.

The GRAPH Menu y(x)=

Chapter 6 describes these GRAPH menu items: ZOOM, TRACE, MATH, DRAW, STGDB, RCGDB, EVAL, STPIC, and RCPIC.

WIND

ZOOM

6 TRACE GRAPH

4

MATH

DRAW FORMT STGDB RCGDB

4

EVAL

STPIC

RCPIC

y(x)=

Displays the equation editor; use this screen to enter functions to be graphed

WIND

Displays the window editor; use this editor to change graph screen dimensions

ZOOM

Displays the GRAPH ZOOM menu; use these items to change the graph screen dimensions

TRACE

Activates the trace cursor; use this cursor to trace along the graph of a specific function

GRAPH

Displays the graph screen; graphs all selected functions and turned on stat plots

MATH

Displays the GRAPH MATH menu; use this menu to explore graphs mathematically

DRAW

Displays the GRAPH DRAW menu; use this menu to draw on graphs or test pixels

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76

Chapter 5: Function Graphing FORMT

Displays the graph format screen; use this screen to select graph format settings

STGDB

Displays the Name= prompt and STGDB menu; use this prompt to enter a GDB variable

RCGDB

Displays the Name= prompt and RCGDB menu; use this menu to recall a graph database

EVAL

Displays the Eval x= prompt; enter an x for which you want to solve the current function

STPIC

Displays the Name= prompt and STPIC menu; use this prompt to enter a PIC variable

RCPIC

Displays the Name= prompt and RCPIC menu; use this menu to recall a picture

Using the Equation Editor To display the equation editor in Func graphing mode, select y(x)= from the GRAPH menu (6 &). The GRAPH menu shifts up and the equation editor menu is displayed as the lower menu. You can store up to 99 functions in the equation editor, if sufficient memory is available. If a function is selected, its equals sign (=) is highlighted in the equation editor. If the function is deselected, its equals sign is not highlighted. Only selected functions are plotted when the TI-86 plots a graph. The Equation Editor (GRAPH y(x)=) Menu y(x)= x

WIND y

ZOOM INSf

TRACE GRAPH DELf SELCT

6& 4

ALL+

ALLN

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STYLE

Chapter 5: Function Graphing x

Pastes the variable x to the current cursor location (same as 2 or - n ãXä )

y

Pastes the variable y to the current cursor location (same as - n ãYä )

INSf

Inserts a deleted equation variable (function) name above the current cursor location (only the variable name is inserted)

DELf

Deletes the function that the cursor is on

SELCT

Changes the selection status of the function that the cursor is on (selects or deselects)

ALL+

Selects all defined functions in the equation editor

ALLN

Deselects all defined functions in the equation editor

STYLE

Assigns the next of seven available graph styles to the function that the cursor is on

Defining a Function in the Equation Editor To move from the first equation editor function to the last, press $. To move to the beginning or end of an equation, press - ! or - ".

77



Display the equation editor.

6&



If functions are stored in the equation editor, move the cursor down until a blank function is displayed.

( # or b)



Enter an equation in terms of x to define the function. When you enter the first character, the function is selected automatically. (The function’s equals sign is highlighted.)

4=2



Move the cursor to the next function.

b or #

An ellipsis indicates that an equation continues beyond the screen.

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Chapter 5: Function Graphing

You can edit expressions you inserted using Rcl.

Notes about Defining Function Equations ♦ You can include functions, variables, constants, matrices, matrix elements, vectors, vector elements, lists, list elements, complex values, or other equations in the equation. ♦ If you include matrices, vectors, or complex values, the equation must evaluate to a real number at each point. ♦ You can include another defined function in an equation. For example, given y1=sin x and y2=4+y1, the function y2 would equal 4 plus the sine of x. ♦ To enter a function name, select y from the equation editor menu, and then enter the appropriate number. ♦ To insert the contents of an equation variable, use RCL (Chapter 1). To enter the equation variable at the Rcl prompt, use the ALPHA keys, alpha keys, and other character keys. ♦ To select all functions from the home screen or in the program editor, select FnOn from the CATALOG (or enter the individual characters) and press b. ♦ To select specific functions from the home screen or in the program editor, select FnOn from the CATALOG (or enter the individual characters), enter the number of each function, and press b. For example, to select y1, y3, and y5, enter FnOn 1,3,5. ♦ To deselect functions from the home screen or in the program editor, use FnOff the same way you use FnOn to select functions. ♦ When a function evaluates to a non-real number, the value is not plotted on the graph; no error is returned.

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Chapter 5: Function Graphing

The TI-86 graphs all selected functions on the same graph screen.

79

Selecting Graph Styles Depending on which graphing mode is set, the TI-86 offers up to seven distinct graph styles. You can assign these styles to specific functions to visually differentiate each from the others. For example, you can show y1 as a connected line (»y1= in the equation editor) and y2 as a dotted line (Ây2=), and shade the area above y3 (¾y3=). Also, you can manipulate the styles to illustrate actual phenomena graphically, such as a ball flying through the air (using Á) or the circular movement of a chair on a Ferris wheel (using À).

¾ (shade above) and ¿ (shade below) are available only in Func graphing mode.

 (dot) is available in all graphing modes except DifEq graphing mode.

Icon Style

Characteristics of the Plotted Function

» ¼ ¾ ¿ À Á Â

Line

A solid line connects each plotted point; this is the default in Connected mode

Thick

A thick solid line connects each plotted point

Above

Shades the area above the function

Below

Shades the area below the function

Path

A circle cursor traces the leading edge of the function and draws a path as it plots

Animate A circle cursor traces the leading edge of the function as it plots; does not draw a path Dot

A small dot represents each plotted point; this is the default in Dot mode

To set the graph style from a program, select GrStl( from the CATALOG (A to Z Reference).

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Chapter 5: Function Graphing

Setting the Graph Style in the Equation Editor In the example, ¾ (shade above) is selected for y2. All window variables are set to the default values (page 82).

If you assign ¾ or ¿ to a function that graphs a family of curves (page 86), the same pattern rotation applies to the members of the family of curves.



Display the equation editor.

6&



Move the cursor to the function or functions for which you want to set the graph style.

#



Display the equation editor menu item STYLE.

/



Select STYLE repeatedly to scroll the graph style icons to the left of the equation name.

((



View the graph with the new graph style.

-*



Clear the GRAPH menu to view the graph only.

:

Using Shading Patterns to Differentiate Functions When you select ¾ (shade above) or ¿ (shade below) for more than one function, the TI-86 rotates through a series of four shading patterns. ♦ First shaded function: vertical lines ♦ Second shaded function: horizontal lines ♦ Third shaded function: negatively sloping diagonal lines ♦ Fourth shaded function: positively sloping diagonal lines The rotation returns to vertical lines for the fifth shaded function and repeats the order.

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Chapter 5: Function Graphing

81

Viewing and Changing OnàOff Status of Stat Plots Plot1 Plot2 Plot3 on the top line of the equation editor displays the onàoff status of each stat plot (Chapter 14). When a plot name is highlighted on this line, the plot is on. To change the onàoff status of a stat plot from the equation editor, press $, ", and ! to place the cursor on Plot1, Plot2, or Plot3, and then press b.

Setting the Window Variables The graph screen window represents the portion of the coordinate plane displayed on the graph screen. By setting window variables, you can define the graph screen window boundaries and other attributes. xMin, xMax, yMin, and yMax are the graph screen boundaries. To remove tick marks from both axes, set xScl=0 and yScl=0.

Small xRes values improve graph resolution but may cause the TI-86 to plot graphs more slowly.

xScl (x scale) is the number of units represented by the distance from one tick mark to the next

tick mark on the x-axis. yScl (y scale) is the number of units represented by the distance from one tick mark to the next tick mark on the y-axis. xRes sets pixel resolution for function graphs only, using integers 1 through 8. ♦ At xRes=1 (the default), functions are evaluated and graphed at each pixel on the x-axis. ♦ At xRes=8, functions are evaluated and graphed at every eighth pixel along the x-axis.

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Chapter 5: Function Graphing

Displaying the Window Editor To display the window editor, select WIND from the GRAPH menu (6 '). Each graphing mode has a unique window editor. The window editor to the right shows the default values in Func graphing mode. $ indicates that xRes=1 (x resolution) is below yScl on the window editor. Changing a Window Variable Value

Display the window editor.

6'

both must be true to graph successfully.



Move the cursor to the window variable you want to change.

###

In the example, yMin is changed to 0.



Edit the value, which can be an expression.

0



Evaluate any expressions and store the value.

b or #

xMin
To change a window variable value from the home screen or in the program editor, enter the value, and then press X. Either select the window variable from the VARS WIND screen ( - w / / WIND) or enter individual characters. Press b.

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Chapter 5: Function Graphing

83

Setting Graphing Accuracy with @x and @y The window variables @x and @y define the distance from the center of one pixel to the center of any adjacent pixel. When you display a graph, the values of @x and @y are calculated from xMin, xMax, yMin, and yMax using these formulas: @x=(xMin+xMax)à126 @y=(yMin+yMax)à62 @x and @y are not on the window editor. To change them, you must follow the steps above

for changing a window variable value from the home screen or in the program editor. When you change the values stored to @x and @y, the TI-86 automatically recalculates xMax and yMax from @x, xMin, @y, and yMin, and the new values are stored.

Setting the Graph Format The TI-86 retains independent format settings for each graphing mode. In DifEq graphing mode, the graph format screen key sequence is 6 / & (Chapter 10).

To display the graph format screen, select FORMT from the GRAPH menu (6 / (). The graph format settings define various characteristics of the displayed graph. The current settings are highlighted. To change a setting, move the cursor onto the new setting, and then press b, the same as on the mode screen.

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84

Chapter 5: Function Graphing

DifEq graphing mode has a

unique set of graph format settings (Chapter 10).

Grid points cover the graph screen in rows that correspond to the tick marks on each axis.

RectGC

Displays the cursor location as rectangular graph coordinates x and y; when RectGC is set, plotting the graph, moving the free-moving cursor, and tracing update x and y; if CoordOn format also is selected, x and y are displayed

PolarGC

Displays the cursor location as polar graph coordinates R and q; when PolarGC is set, plotting the graph, moving the free-moving cursor, and tracing update x, y, R and q; if CoordOn format also is selected, R and q are displayed

CoordOn

Displays the cursor coordinates at the bottom of the graph

CoordOff

Does not display the cursor coordinates at the bottom of the graph

DrawLine

Draws a line between the points calculated for the functions in the equation editor

DrawDot SeqG

Plots only the calculated points for the functions in the equation editor (sequential graphing) Evaluates and plots one function completely before evaluating and plotting the next function

SimulG

(simultaneous graphing) Evaluates and plots all selected functions for a single value of x and then evaluates and plots them for the next value of x

GridOff

Omits the grid points from the display

GridOn

Displays grid points

AxesOn

Displays the axes

AxesOff

Omits the axes from the display; AxesOff overrides the LabelOffàLabelOn format setting

LabelOff

Omits the axis labels from the display

LabelOn

Labels the axes, if AxesOn is also selected; x and y for Func, Pol, and Param modes; various labels in DifEq mode

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Chapter 5: Function Graphing

85

Displaying a Graph In the example graph to the right, all default settings related to graphing are set.

To view the graph without the GRAPH menu on the bottom

line, press : after plotting the graph.

To display a graph, select GRAPH from the GRAPH menu. The graph screen is displayed. If the graph is newly defined, the busy indicator is displayed at the top-right corner as the TI-86 draws the graph. ♦ In SeqG format, the TI-86 draws each selected function one by one, in function-name order (for example, y1 is graphed first, y2 is graphed second, and so on). ♦ In SimulG format, the TI-86 draws all selected graphs simultaneously. You can display and explore a graph from a program (Chapter 16). To use graphing commands on the home screen, select them from the CATALOG or entering the individual characters.

When you pause, the busy indicator in the top-right corner becomes a dotted line.

Pausing or Stopping a Graph in Progress ♦ To pause graph plotting, press b. To resume plotting, press b again. ♦ To stop graph plotting, press ^. To replot, select GRAPH from the GRAPH menu. Modifying a Drawn Graph To remove these items from the graph screen:

Press (or select):

Cursor, coordinate values, or menus (To restore menus, press . or 6)

:

Free-moving cursor and coordinate values but not the menus

b

Cursor and coordinate values but not the menus

6 or GRAPH

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86

Chapter 5: Function Graphing

Graphing a Family of Curves If you enter a list as an element in an equation, the TI-86 plots the function for each value in the list, graphing a family of curves. In SimulG graphing order mode, the TI-86 graphs all functions sequentially for the first element in each list, then for the second element, and so on. When you use more than one list in an expression, all lists must have the same dimension.

For example, {2,4,6} sin x graphs three functions: 2 sin x, 4 sin x, and 6 sin x.

The equation {2,4,6} sin ({1,2,3} x) also graphs three functions: 2 sin x, 4 sin (2x), and 6 sin (3x).

Smart Graph Smart Graph displays the previously displayed graph when you press 6, as long as all factors that would cause replotting are unchanged since the graph was last displayed. Smart Graph replots if you performed any of these actions since the graph was last displayed. ♦ Changed a mode setting that affects graphs ♦ Changed a function or stat plot that was plotted on the last graph screen ♦ Selected or deselected a function or stat plot ♦ Changed the value of a variable in a selected function ♦ Changed the value of a window variable setting ♦ Changed a graph format setting

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6

Graph Tools TI-86

Graph Tools on the TI-86................................................... 88 Tracing a Graph ................................................................. 90 Resizing the Graph Screen with ZOOM Operations ........... 91 Using Interactive Math Functions ...................................... 95 Evaluating a Function for a Specified x............................ 101 Drawing on a Graph ........................................................ 101

M1

M2

M3

M4

M5

F1

F2

F3

F4

F5

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88

Chapter 6: Graph Tools

Graph Tools on the TI-86 Chapter 5 describes how to use the GRAPH menu items y(x)=, WIND, GRAPH, and FORMT to define and display the graph of a function in Func graphing mode. This chapter describes how to use the other GRAPH menu items to apply preset graph screen dimensions, explore the graph and trace specific functions, perform mathematical analyses, draw on graphs, and store and recall graphs and drawings. You can use most graph tools in all four graphing modes. The GRAPH Menu This is the GRAPH menu in Func graphing mode. The GRAPH menu differs slightly from graphing mode to graphing mode.

y(x)=

WIND

6 ZOOM

TRACE GRAPH

4

MATH

DRAW FORMT STGDB RCGDB

4

EVAL

STPIC

RCPIC

ZOOM

Displays the GRAPH ZOOM menu; use these items to apply preset graph screen dimensions

TRACE

Activates the trace cursor; use this cursor to trace along graphs of specific functions

MATH

Displays the GRAPH MATH menu; use this menu to explore graphs mathematically

DRAW

Displays the GRAPH DRAW menu; use this menu to draw on graphs

STGDB

Displays the Name= prompt and GDB menu; use this prompt to enter a GDB variable

RCGDB

Displays the Name= prompt and GDB menu; use this menu to recall a GDB variable

EVAL

Displays the Eval x= prompt; use this prompt to enter an x value for which you want to solve the current function

STPIC

Displays the Name= prompt and PIC menu; use this prompt to enter a PIC variable

RCPIC

Displays the Name= prompt and PIC menu; use this menu to recall PIC variable

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Chapter 6: Graph Tools

In the example, the function y(x)=x^3+.3x 2-4x is graphed.

The numeric display mode settings do not affect coordinate display.

89

Using the Free-Moving Cursor When you select GRAPH from the GRAPH menu, the graph screen is displayed with the free-moving cursor at the center of the screen. The cursor appears as a plus sign with a flashing center pixel. To move the cursor, press ", #, !, or $; it moves in the direction of the cursor key you press. ♦ In RectGC format, each cursor movement updates the variables x and y. In PolarGC format, each cursor movement updates x, y, R, and q. ♦ In CoordOn format, the x and y cursor coordinates are displayed at the bottom of the graph screen as you move the cursor. Graphing Accuracy The coordinate values displayed as you move the cursor approximate actual mathematical coordinates, accurate to within the width and height of the pixel. As the difference between xMin and xMax and between yMin and yMax becomes smaller (for example, when you zoom in on a graph), graphing is more accurate and coordinate values approximate the actual mathematical coordinates more closely. The free-moving cursor coordinates represent the cursor location on the graph screen. Moving the free-moving cursor precisely from one plotted point to the next along a function is very difficult. To move along a function easily, use the trace cursor (page 90).

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Chapter 6: Graph Tools

Tracing a Graph To display the graph and begin a trace, select TRACE from the GRAPH menu. In the example, the function y(x)=x^3+.3x 2-4x is graphed.

The trace cursor appears as a small square with a flashing diagonal line at each corner. Initially, the trace cursor appears on the first selected function, at the x value closest to the middle of the screen. If CoordOn format is selected, the cursor coordinates are displayed at the bottom of the screen.

When you enter the first character of an independent variable value, an x= prompt is displayed (or q= or t=). The value can be an expression.

If the function is undefined at an x value, then the y value is blank.

To move the trace cursor...

Press these keys:

To the next larger or next smaller plotted point in a function

" or !

To any valid independent-variable value (x, q, or t) on the current equation

value b

From one function to another function at x, in the order or reverse order of the selected functions in the equation editor

# or $

From one member to another member of a family of curves (Chapter 5)

# or $

As you move the trace cursor along a function, the y value is calculated from the x value. That is, y=yn(x). When you trace beyond the top or bottom of the graph screen, the coordinates displayed on the screen continue to change as if the cursor were still on the screen. Panning: To view function coordinates to the left or right of the current graph screen, press and hold ! or " while tracing. When you pan beyond the left or right side of the screen during a trace, the TI-86 automatically changes the values of xMin and xMax.

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Chapter 6: Graph Tools

91

Quick Zoom: While tracing, you can press b to adjust the graph screen so that the trace cursor location becomes the center of a new graph screen, even if you have moved the cursor beyond the top or bottom of the display. In effect, this is vertical panning. Stopping and Resuming a Trace To stop tracing and restore the free-moving cursor, press : or 6. To resume tracing, select TRACE from the GRAPH menu. If Smart Graph has not replotted the graph (Chapter 5), the trace cursor is at the point where you stopped tracing.

Resizing the Graph Screen with ZOOM Operations To view the current window variable values, select WIND from the GRAPH menu.

The standard TI-86 graph screen displays the portion of the xy plane defined by the values stored to the window variables. With the GRAPH ZOOM menu items, you can change some or all of the window variable values and redisplay the graph, usually with one keystroke. As a result, a smaller or larger portion of the xy plane is displayed. The GRAPH ZOOM Menu y(x)= BOX

WIND ZIN

ZOOM ZOUT

6( TRACE GRAPH ZSTD ZPREV

4

ZFIT

ZSQR

4

ZRCL

ZFACT ZOOMX ZOOMY

4

ZSTO

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ZTRIG ZDECM ZDATA ZINT

92

Chapter 6: Graph Tools

To cancel the effect of any ZOOM menu item and return to the default window variable values, select ZSTD.

If you graph a circle but it appears elliptical, you can use ZSQR to reset the window variable values so that the circle graph appears circular.

BOX

Draws a box to define the graph screen

ZIN

(zoom in) Magnifies the graph around the cursor by factors of xFact and yFact

ZOUT

(zoom out) Displays more of the graph around the cursor by factors of xFact and yFact

ZSTD

Displays the graph in standard dimensions; resets the default window variable values

ZPREV

Reverses the last zoom operation; window variables revert to previous values

ZFIT

Recalculates yMin and yMax to include the minimum and maximum y values of the selected functions between the current xMin and xMax

ZSQR

Sets equal-size pixels on the x-axis and y-axis; adjusts window variable values in one direction so that @[email protected], while xScl and yScl remain unchanged; the midpoint of the current graph (not the axes intersection) becomes the midpoint of the new graph

ZTRIG

Sets built-in window variables appropriate for trigonometric functions in Radian mode: xMin=L8.24668071567 xScl=1.5707963267949 (p à2) yMax=4 xMax=8.24668071567

yMin=L4

yScl=1

ZDECM

Sets @x=.1, @y=.1, xMin=L6.3, xMax=6.3, xScl=1, yMin=L3.1, yMax=3.1, and yScl=1

ZDATA

Sets window variable values to display all statistical data points; adjusts xMin and xMax only; applies to histograms, scatter plots, and stat plots only (Chapter 14)

ZRCL

Uses window variable values stored in the user-defined zoom-window variables (ZSTO)

ZFACT

Displays the ZOOM FACTORS screen

ZOOMX

Zooms out by a factor of xFact only; ignores yFact (page 93)

ZOOMY

Zooms out by a factor of yFact only; ignores xFact

ZINT

Sets integer values on the axes; sets @x=1, @y=1, xScl=10, and yScl=10; the current cursor becomes the center of the new graph screen after you press b

ZSTO

Stores current window variable values to user-defined zoom-window variables (ZRCL)

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Chapter 6: Graph Tools

93

Defining a Custom Zoom In Using BOX, you can zoom in on any rectangular area within the current graph screen. Before you begin these steps, enter a function in the equation editor. In the example, the function y(x)=x^3+.3x 2N4x is graphed.



Select BOX from the GRAPH ZOOM menu. The zoom cursor is displayed at center screen.

6( &



Move the cursor to any spot you want to define as a corner of the zoom box; mark the corner with a small square.

"#!$ b

To cancel BOX without redefining the graph screen, press :.



Move the cursor away from the first corner, creating an adjustable box whose diagonal corners are the small square and the cursor.

"#!$

When you replot the graph, the TI-86 updates the window variable values.



When you have defined the box, replot all selected functions in the new graph screen.

b



Clear the menus from the screen.

:

To store to xFact or yFact from the home screen or in the program editor, you can select it from the VARS ALL screen or enter it using ALPHA and alpha keys.

Setting Zoom Factors Zoom factors define the magnification or reduction factor by which ZIN, ZOUT, ZOOMX, and ZOOMY zoom in or zoom out around a point. To display the zoom factors editor, select ZFACT from the GRAPH ZOOM menu (press 6 ( / / '). xFact and yFact must be ‚ 1. The default value for both factors is 4 in all graphing modes. Zooming In and Zooming Out on a Graph ZIN magnifies the part of the graph surrounding the cursor location. ZOUT displays a greater portion of the graph, centered on the cursor location. xFact and yFact determine the extent. The steps below describe how to use ZIN. To use ZOUT, select it instead of ZIN in step 2.

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Chapter 6: Graph Tools

In the example, the function y(x)=x^3+.3x 2N4x is graphed.



Check xFact and yFact; change as needed.

6( // '

When you select a ZOOM feature, Smart Graph displays the current graph.



Select ZIN from the GRAPH ZOOM menu to display the zoom cursor.

('



Move the zoom cursor to the intended new center point of the graph screen.



Zoom in. The TI-86 adjusts the graph screen by xFact and yFact, updates window variable values, and replots the selected functions centered on the cursor location.

To cancel a zoom before you complete it, press :.

"#!$

b

You can continue to zoom in (or zoom out) on the current graph, unless you press a key other than b, ", #, !, or $. ♦ To zoom in (or zoom out) again at the same point, press b. ♦ To zoom in (or zoom out) at a new center point, move the cursor and press b. To zoom out only on the horizontal axis by a factor of xFact, select ZOOMX instead of ZIN in step 2 above. ZOOMX plots the selected functions centered on the cursor location and updates some window variable values; yMin and yMax are unchanged. To zoom out only on the vertical axis by a factor of yFact, select ZOOMY instead of ZIN in step 2 above. ZOOMY plots the selected functions centered on the cursor location and updates some window variable values; xMin and xMax are unchanged.

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Chapter 6: Graph Tools

You can select all zoomwindow variables from the VARS WIND screen in any graph mode. You also can enter the variable characters individually. The zoom-window variables resume their standard default values when you reset defaults.

Storing and Recalling Zoom-Window Variable Values ♦ To store all current zoom-window variable values simultaneously as a user-defined custom zoom feature, select ZSTO from the GRAPH ZOOM menu. ♦ To execute a user-defined custom zoom, which resets the graph screen to the stored zoom-window variables, select ZRCL from the GRAPH ZOOM menu. Using ZSTO in these graphing modes: Stores to these zoom-window variables: Func, Pol, Param, and DifEq graphing modes

zxMin, zxMax, zxScl, zyMin, zyMax, and zyScl

Pol graphing mode only

zqMin, zqMax, and zqStep

Param graphing mode only

ztMin, ztMax, and ztStep

DifEq graphing mode only

ztMin, ztMax, ztStep, and ztPlot

Using Interactive Math Functions When you select a GRAPH MATH operation, Smart Graph displays the current graph with the trace cursor. To perform the GRAPH MATH operation, press # and $ to move to the function. When a GRAPH MATH menu operation prompts you to specify left bound, right bound, and guess, the accuracy of the values you specify will affect the length of time the TI-86 spends calculating the answer; the better the guess, the shorter the calculation time. The GRAPH MATH Menu MATH ROOT

6/&

DRAW FORMT STGDB RCGDB dyàdx FMIN FMAX ‰f(x)

4

INFLC

4

TANLN

YICPT

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ISECT

DIST

ARC

96

Chapter 6: Graph Tools

The GRAPH MATH menu differs slightly for Pol and Param graphing modes (Chapters 8 and 9). DifEq graphing mode has no GRAPH MATH menu.

ROOT

Finds the root of a function using a specified left bound, right bound, and guess

dyàdx

Finds a numeric derivative (slope) of a function at the trace cursor location

‰f(x)

Finds a function’s numerical integral using a specified left bounds and right bound

FMIN

Finds a function’s minimum using a specified left bound, right bound, and guess

FMAX

Finds a function’s maximum using a specified left bound, right bound, and guess

INFLC

Finds a function’s inflection point using a specified left bound, right bound, and guess

YICPT

Finds a function’s y-intercept (y at x=0)

ISECT

Finds the intersection of two functions using a specified left bound, right bound, and guess

DIST

Finds the straight-line distance between a specified left bound and right bound

ARC

Finds the distance along a function between two specified points on the function

TANLN

Draws the tangent line at a specified point

Settings That Affect GRAPH MATH Operations ♦ The tolerance variable tol (Appendix) affects the accuracy of ‰f(x), FMIN, FMAX, and ARC. Accuracy increases as the tolerance value becomes smaller. ♦ The step-size variable d (Appendix) affects the accuracy of dyàdx, INFLC in dxNDer differentiation mode (Chapter 1), ARC, and TANLN. Accuracy increases as the step-size value becomes smaller. ♦ The differentiation mode setting affects dyàdx, INFLC, ARC, and TANLN; dxDer1 (exact) mode is more accurate than dxNDer (numeric) mode (Chapter 1).

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Chapter 6: Graph Tools

97

Using ROOT, FMIN, FMAX, or INFLC The steps for ROOT, FMIN, FMAX, and INFLC are the same, except for the menu selection in step 1. In the example, the function y(x)=x^3+.3x 2N4x is selected. Step 2 is not necessary here because only one function is selected.



Select ROOT from the GRAPH MATH menu. A Left Bound? prompt is displayed.

6/ &&



Move the cursor onto the function for which you want to find a root.

#$

When you enter a value directly for the left bound, right bound, or guess, an x= prompt is displayed on the bottom of the graph screen.



Specify the left bound for x. Either move the trace cursor to the left bound or enter a value directly. Right Bound? is displayed.

a 3 b (or ! " b)



Specify the right bound for x as in step 3. Guess? is displayed.

a 1 b (or ! " b)



Guess an x value near the root between the left bound and the right bound. Either move the cursor or enter a value.

! " (or a 2)



Solve for x. The result cursor is displayed at the solution point, the cursor coordinate values are displayed, and the x value is stored in Ans.

b

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Chapter 6: Graph Tools

Using ‰f(x), DIST, or ARC The steps for using ‰f(x), DIST, and ARC are the same, except for the menu selection in step 1. In the example, the function y(x)=x^3+.3x 2N4x is selected. Steps 2 and 4 are not necessary here because only one function is selected.

For DIST, when you are specifying the right bound, a line is drawn from the left bound to the right bound.



Select DIST from the GRAPH MATH menu. The current graph is displayed with a Left Bound? prompt.

6/ &/)



Move the cursor onto the function on which the left bound is a point.

#$



Select the left bound for x. Either move the cursor to the left bound or enter the x value. Right Bound? is displayed.

! " b or value b



(DIST only) If you want the right bound to be a point on another function, move the cursor to the other function.

#$



Select the right bound. Either move the cursor to the right bound or enter its x value.

! " or value



b Solve. For DIST, the solution DIST= is displayed and stored in Ans. ♦ For ARC, the solution ARC= is displayed and stored in Ans. ♦ For ‰f(x), the solution ‰f(x)= is displayed, shaded, and stored in Ans. The function integral error value is stored to the variable fnIntErr (Appendix). To remove the shading, select CLDRW from the GRAPH DRAW menu (page 103).



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Chapter 6: Graph Tools

99

Using dyàdx or TANLN The steps for using dyàdx and TANLN are the same, except for the menu selection in step 1. In the example, the function y(x)=x^3+.3x 2N4x is selected.



Select dyàdx from the GRAPH MATH menu. The current graph is displayed.

6/ &'

Move the cursor to the function with the point for which you want to find the derivative, or slope.

#$

TANLN (GRAPH MATH menu) and TanLn (GRAPH DRAW



!"

menu) both draw a tangent line on the graph; only TANLN displays the solution, dyàdx.



Move the cursor to the point (or enter the x value).

b Solve. ♦ For dyàdx, the solution dyàdx= is displayed and stored in Ans. ♦ For TANLN, a tangent line also is displayed. To remove the tangent line and dyàdx= prompt, select CLDRW from the GRAPH DRAW menu.

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Chapter 6: Graph Tools

Using ISECT In the example, the functions y(x)=x^3+.3x 2N4x and y(x)=x 2+3xN3 are selected.



Select ISECT from the GRAPH MATH menu. The current graph is displayed with First Curve? at the bottom of the graph screen.

6/ &/(



Select the first function (curve). The cursor moves to the next function and Second Curve? is displayed.

#$b



Select the second function (curve). Guess? is displayed.

#$b



Guess the intersection. Either move the cursor to a point near an intersection or enter an x value.

a1`5 (or ! ")



Solve. The result cursor is displayed at the intersection , the cursor coordinates are the result, and the x value is stored to Ans.

b

Using YICPT To use YICPT, select YICPT from the GRAPH MATH menu (6 / & / '). Press # and $ to select a function, and then press b. The result cursor is displayed at the y-intercept, the cursor coordinate values are displayed, and y is stored in Ans.

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Chapter 6: Graph Tools

101

Evaluating a Function for a Specified x To clear entered numbers from the Eval x= prompt, press :.



Select EVAL from the GRAPH menu. The graph is displayed with the Eval x= prompt in the bottom-left corner.

6/ /&

To cancel EVAL, press : after clearing the Eval x= prompt.



Enter a real x value between window variables xMin and xMax.

`5-~



Evaluate. The result cursor is on the first selected function at the entered x value. The coordinate values are displayed. The number in the top-right corner indicates which function is evaluated.

b



Move the result cursor to the next or previous selected function. The result cursor is on the next or previous function at entered x value, the coordinate values are displayed, and the function number changes.

$#

Expressions are valid for x.

You may continue to enter valid x values for which to evaluate the selected functions.

Drawing on a Graph You can use the drawing tools (except DrInv) to draw points, lines, circles, shaded areas, and text on the current graph in any graphing mode. The drawing tools use the display’s xand y-coordinate values.

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Chapter 6: Graph Tools

Before Drawing on a Graph All drawings are temporary; they are not stored in a graph database. Any action that causes Smart Graph to replot the graph erases all drawings. Therefore, before you use any drawing tool, consider whether you want to perform any of these graphing activities first. ♦ Change a mode setting that affects graphs ♦ Select, deselect, or edit a current function or stat plot ♦ Change the value of a variable used in a selected function ♦ Change a window variable value ♦ Change a graph format setting or graph style ♦ Clear current drawings with CLDRW

Graph database (GDB) and picture (PIC) variable names can be from one to eight characters long. The first character must be a letter.

Saving and Recalling Drawn Pictures To store the elements that define the current graph to a graph database (GDB) variable, select STGDB from the GRAPH menu. These information types are stored to a GDB variable: ♦ Equation editor functions ♦ Window variable values ♦ Graph style settings ♦ Format settings To recall the stored GDB later, select RCGDB from the GRAPH menu, and then select the GDB variable from the GRAPH RCGDB menu. When you recall a GDB, the information stored in the GDB replaces any current information of these types.

The next section describes how to draw lines, points, curves, and text onto a graph; you then can store the drawings to a PIC variable.

To store the current graph display, including drawings, to a picture (PIC) variable, select STPIC from the GRAPH menu. Only the graph picture is stored to the specified PIC variable. To superimpose one or more stored graph pictures onto a graph later, select RCPIC from the GRAPH menu, and then select the PIC variable from the GRAPH RCPIC menu.

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Chapter 6: Graph Tools

103

Clearing Drawn Pictures To clear drawn pictures while the graph is displayed, select CLDRW from the GRAPH DRAW menu. The graph is replotted and displayed with no drawn elements. To clear drawn pictures from the home screen, select ClDrw from the CATALOG. ClDrw is pasted to the cursor location. Press b. Done is displayed; when you display the graph again, no drawings are displayed. The GRAPH DRAW Menu DrInv is not available in Pol, Param, or DifEq graphing

MATH Shade

6/'

DRAW FORMT STGDB RCGDB LINE VERT HORIZ CIRCL

4

DrawF

PEN

PTON

PTOFF PTCHG

4

CLDRW

PxOn

PxOff

PxChg

4

TEXT

TanLn

DrInv

modes.

PxTest

You can use these GRAPH DRAW menu items only on the home screen or in the program editor. For PxOn, PxOff, PxChg, and PxTest, row and column are integers, where 0row62 and 0column126. For DrawF, TanLn, and DrInv, expression is in terms of x. Also, you cannot include a list in expression to draw a family of curves.

Shade(

Shades a specified area of a graph (See page 104)

DrawF expression

Draws expression as a function

PxOn(row,column)

Turns on the pixel at (row,column)

PxOff(row,column)

Turns off the pixel at (row,column)

PxChg(row,column)

Changes the onàoff status of the pixel at (row,column)

PxTest(row,column)

Returns 1 if the pixel at (row,column) is on, or 0 if the pixel is off

TanLn(expression,x)

Draws expression as a function and a tangent line of expression at x

DrInv expression

Draws the inverse of expression

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Chapter 6: Graph Tools

Shading Areas of a Graph To shade an area of a graph, the syntax is: Shade(lowerFunc,upperFuncã,xLeft,xRight,pattern,patternResä) To replicate the example without additional graphs, turn off all equations and stat plots before entering the instructions as shown.

pattern specifies one of four shading patterns. 1 2 3 4

vertical (default) horizontal negative slope( 45¡) positive slope (45¡)

patternRes specifies one of eight shading resolutions. 1 every pixel (default) 2 every second pixel 3 every third pixel 4 every fourth pixel 5 every fifth pixel 6 every sixth pixel 7 every seventh pixel 8 every eighth pixel

♦ ♦ ♦

The area that is specifically above lowerFunc and below upperFunc is shaded. xLeft > xMin and xRight < xMax must be true. xLeft and xRight specify left and right bounds for shading. (xMin and xMax are defaults.)

These GRAPH DRAW menu items are interactive. Also, you can use all of them, except PEN, on the home screen or in a program (A to Z Reference). LINE

Draws a line segment from one point to another point you specify with the cursor

VERT

Draws a vertical line, which you can move to any displayed x value

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Chapter 6: Graph Tools HORIZ

Draws a horizontal line, which you can move to any displayed y value

CIRCL

Draws a circle with a center point and radius you specify with the cursor

PEN

Draws the path of the cursor as you move it on the graph screen

PTON

Turns on the point at the cursor location

PTOFF Turns off the point at the cursor location PTCHG Changes the onàoff status of a point at the cursor location CLDRW Clears all drawings from the graph screen; replots the graph TEXT

Draws characters on the graph at the cursor location

Drawing a Line Segment In the example, the functions y(x)=x^3+.3x2N4x and y(x)=x2+3xN3 are selected.



Select LINE from the GRAPH DRAW menu. The graph is displayed. Define one segment endpoint with the cursor.

6/ '' "#!$ b



Define the other endpoint of the segment. As you move the cursor, a line anchored at the first defined endpoint extends to the cursor.

"#!$



Draw the line.

b

To draw more line segments, repeat steps 2 and 3; to cancel LINE, press :.

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105

106

Chapter 6: Graph Tools

Drawing a Vertical or Horizontal Line In the example, the function y(x)=x^3+.3x 2N4x is selected. Also, ZIN was executed once with the zoom cursor at (0,0), xFact=2, and yFact=2.



Select VERT (or HORIZ) from the GRAPH DRAW menu. The graph is displayed and a vertical or horizontal line is drawn at the cursor.

6/ '( (or ))



Move the line to the x value (or to the y value, if horizontal) through which you want the line to pass.

!" (or $ #)



Draw the line on the graph.

b

To draw more lines, repeat steps 2 and 3; to cancel VERT or HORIZ, press :. Drawing a Circle In the example, the function y(x)=x^3+.3x 2N4x is selected. Also, ZIN was executed once

with the zoom cursor at (0,0),



Select CIRCL from the GRAPH DRAW menu. The graph is displayed.

6/' *



Define the center point of the circle with the cursor.

"#!$ b



Move the cursor to any point on the intended circumference.

"#!$



Draw the circle.

b

xFact=2, and yFact=2.

Here the circle appears as a circle, regardless of window variable values. When you use Circl( from the CATALOG to draw a circle, the current window variable values may distort the shape.

To draw more circles, repeat steps 2 through 4; to cancel CIRCL, press :.

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Chapter 6: Graph Tools

For DrawF, TanLn, and DrInv, you can use as expression any variable to which a valid expression is stored (including deselected equation variables).

107

Drawing a Function, Tangent Line, or Inverse Function For DrawF, TanLn, and DrInv, expression is in terms of x. When you select DrawF, TanLn, or DrInv from the GRAPH DRAW menu, it is pasted to the home screen or program editor. Upon execution, the drawing is returned. DrInv draws the inverse of expression by plotting its x values on the y-axis and its y values on the x-axis. DrInv is available only in Func graphing mode. DrawF expression

TanLn(expression,x)

DrInv expression

DrawF x^3+.3x 2+4x

TanLn(y1,1.5)

DrInv y1

In the illustrations, y1=x^3+.3x 2N4x is selected.

Drawing Freehand Points, Lines, and Curves In the example, the function y(x)=x^3+.3x 2N4x is selected. Also, ZSTD was executed.

To draw a diagonal line or curve, turn on the pen, press b b, press ! $ (or # ", and so on), and repeat.



Select PEN from the GRAPH DRAW menu.

6/' /'



Move the cursor to where you want to begin drawing.

"#!$



Turn on the pen.

b



Draw whatever you want.

"#!$



Turn off the pen.

b

To draw more points, lines, or curves, repeat steps 2 through 5. To cancel, press :.

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Chapter 6: Graph Tools

Placing Text on a Graph This example adds to the PEN example drawing. Before you start, you may want to store the arrows to a picture variable (page 102).

To erase a character when using TEXT, move the TEXT cursor above it and then press 1 ¤ or - n ¤ to overwrite it.



Select TEXT from the GRAPH DRAW menu. The text cursor is displayed.

6/ ' /// &



Move the cursor to where you want to enter text. Text is entered below the text cursor.

"#!$



Set alpha-lock and enter min. (The alpha cursor ( Ï ) is displayed in the top-right corner.

-n1 ãMä ãIä ãNä



Move the cursor to another location.

ãMä ãAä ãXä



Enter max (alpha-lock remains on).

"#!$

Turning On or Turning Off Points In the example, the function y(x)=x^3+.3x 2N4x is selected. Also, ZSTD was executed.

Points are turned on at (L5,5), (5,5), (5,L5), and (L5,L5).



Select PTON (or PTOFF) from the GRAPH DRAW menu.

6/' /(



Move the cursor to where you want to draw (or erase) a point.

"#!$



Turn on (or turn off) the point.

b

To continue drawing points, repeat steps 2 and 3. To cancel PTON, press :.

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7

Tables TI-86

Displaying the Table ........................................................ 110 Setting Up the Table ........................................................ 113 Clearing the Table............................................................ 114

M1

M2

M3

M4

M5

F1

F2

F3

F4

F5

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110

Chapter 7: Tables

Displaying the Table To display the equation editor, press 6 & (Chapter 5).

The table displays the independent values and corresponding dependent values for up to 99 selected functions in the equation editor. Each dependent variable in the table represents a selected function stored in the equation editor for the current graphing mode. TABLE Menu

7

TABLE TBLST table screen table setup editor

The Table In the example, y1=x 2+3x-4 and y2=sin (3x) are selected and all defaults set.

The table abbreviates values in the columns, if necessary.

7& independent variable values

dependent (equation) variable values

variable names

edit line (function name and full value of current cell shown)

current cell table menu

To edit an equation, press $ in the equation’s table column until the cursor highlights the equation variable on the top line, and then press b. The expression stored to the current equation variable is displayed in the edit line.

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Chapter 7: Tables

111

Independent and Dependent Variables in the Table Graphing Mode In DifEq mode, if an equation has an initial conditions list, the table uses the first list element to evaluate the equation (Chapter 10).

Independent Variable

Dependent (Equation) Variables

Func (function)

x

y1 through y99

Pol (polar)

q

r1 through r99

Param (parametric)

t

xt1àyt1 through xt99àyt99

DifEq (differential equation)

t

Q1 through Q9

Navigating the Table To... Display more dependent variables in the table

Do this: Press " or !

Display greater values in any column

Press # (only when Indpnt: Auto is set; page 112)

Set TblStart to a lower value

Press $ in the independent variable column until the cursor moves past the current TblStart (page 112)

Display the equation in the edit line, where you can edit or deselect it

Press ! or " to move the cursor to an equation variable column, hold $ until the cursor highlights the equation name, and then press b; the equation is displayed in the edit line

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112

Chapter 7: Tables

The Table Menus 7 & The table has a unique menu for each graphing mode, as shown below. In Function Graphing Mode

TBLST SELCT

In Parametric Graphing Mode

x

y

q

r

In Polar Graphing Mode

TBLST SELCT

TBLST SELCT

t

xt

In Differential Equation Graphing Mode

TBLST SELCT

t

Q

TBLST

Displays the table setup editor

SELCT

On the edit line, deselects or cancels deselection of the equation

x and y; q and r; t, xt, and yt; or t and Q

On the edit line, pastes the variable to the cursor location; the variables change according to graphing mode

♦ ♦ ♦ ♦

yt

To add an equation to the table, select it in the equation editor (Chapter 5). SELCT only removes equations from the table. To remove an equation from a column in the table, select SELCT from the table menu. Remaining equations that follow the removed equation shift left one column. To deselect an equation with SELCT, the equation and cursor must be displayed in the edit line. If the equation is in the edit line but the cursor is not, press b. To compare two dependent variables not defined consecutively in the equation editor, use SELCT from the table screen menu to deselect the dependent variables in between.

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Chapter 7: Tables

113

Setting Up the Table To display the table using the current table setup settings, select TABLE from the TABLE menu.

To display the table setup editor, select TBLST from the TABLE menu. The screen to the right shows the default table setup settings. TblStart specifies the first independent variable value (x, q, or t) in the table (only when Indpnt: Auto is selected).

TblStart and @Tbl must be

@Tbl (table step) specifies the increment or decrement from one independent variable value

real numbers; you can enter an expression.

to the next independent variable value in the table. ♦ If @Tbl is positive, then the values of x, q, or t increase as you scroll down the table. ♦ If @Tbl is negative, then the values of x, q, or t decrease as you scroll down the table.

In DifEq graphing mode, it is a good practice to set TblStart = tMin and @Tbl = tStep.

Indpnt: Auto displays independent variable values automatically in the first column of the table, starting at TblStart. Indpnt: Ask displays an empty table. As you enter x values in the x= prompt (x=value b), each value is added to the independent variable column and the corresponding dependent variable values are calculated and displayed. When Ask is set, you cannot scroll beyond the six independent variable values that are currently displayed in the table.

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Chapter 7: Tables

Viewing and Editing Dependent Variable Equations 2

In the example, y1=x +3x-4 and y2=sin (3x) are selected and all defaults set.

When you display the equation in the edit line, the column equation name is highlighted.



Display the table.

7&



Move the cursor into the column of the dependent variable you want to edit, and then move up the column until the name is highlighted.

"$



Display the equation in the edit line.

b

Edit the equation.

"""5" \1

Enter the edited equation. b The dependent variable values are recalculated. ♦ The cursor returns to the edited dependent variable’s first value. ♦ The equation editor is updated.



Clearing the Table When you use ClTbl in a program, the table is cleared upon program execution (Chapter 16).

To clear the table when Indpnt: Ask is set, select ClTbl from the CATALOG, and then press b. All independent and dependent variable columns are cleared. ClTbl does nothing when Indpnt: Auto is set.

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8

Polar Graphing TI-86

Preview: Polar Graphing .................................................. 116 Defining a Polar Graph .................................................... 117 Using Graph Tools in Pol Graphing Mode........................ 119

M1

M2

M3

M4

M5

F1

F2

F3

F4

F5

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116

Chapter 8: Polar Graphing

Preview: Polar Graphing The graph of the polar equation A sin (Bq) forms the shape of a flower. Graph the flower for A=8 and B=2.5. Then explore the appearance of the flower for other values of A and B.

Select Pol mode from the mode screen.

-m### #"b



Display the equation editor and polar equation editor menu.

6&



(Deselect or delete all equations if any.) Store r1(q)=8sin(2.5q).



Select ZSTD from the GRAPH ZOOM menu. r1 is plotted on the graph screen.

-g)



Display the window editor, and then change qMax to 4p.

' #4- ~

To remove the GRAPH menu from the graph screen, as shown, press :.



Select ZSQR from the GRAPH ZOOM menu. xMin and xMax are changed to display the graph in correct proportion.

(/'

To redisplay the GRAPH menu, press 6.



Change the values of A and B and redisplay the graph.

& (enter other A and B values)

(/'/) 8=D2`5&E

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Chapter 8: Polar Graphing

117

Defining a Polar Graph The steps for defining a polar graph are similar to the steps for defining a function graph. This chapter assumes that you are familiar with Chapter 5: Function Graphing and Chapter 6: Graph Tools. Chapter 8 details aspects of polar graphing that differ from function graphing. Setting Polar Graphing Mode To display the mode screen, press - m. To graph polar equations, you must select Pol graphing mode before you enter equations, set the format, or edit window variable values. The TI-86 retains separate equation, format, and window data for each graphing mode. The GRAPH Menu Chapter 5 describes these GRAPH menu items: GRAPH and FORMT.

r(q)=

Chapter 6 describes these GRAPH menu items: ZOOM, TRACE, DRAW, STGDB, RCGDB, EVAL, STPIC, and RCPIC.

polar equation editor

WIND

polar window editor

6 ZOOM

TRACE GRAPH

4

MATH

DRAW FORMT STGDB RCGDB

4

EVAL

STPIC

polar graph math menu

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RCPIC

118

Chapter 8: Polar Graphing

Displaying the Polar Equation Editor To display the polar equation editor, select r(q)= from the GRAPH menu in Pol graphing mode (6 &). The polar equation editor menu displayed on the bottom line is the same as the Func mode equation editor menu, except that q and r replace x and y. In this editor, you can enter and display up to 99 polar equations, r1 through r99, if sufficient memory is available. Equations are defined in terms of the independent variable q. The default graph style is » (line) in Pol graphing mode. ¾ (shade above) and ¿ (shade below) graph styles are not available in Pol graphing mode. Setting the Graph Screen Window Variables To display the polar window editor, select WIND from the GRAPH menu (6 '). Pol graphing mode has the same window variables as Func graphing mode, except: ♦ xRes is not available in Pol graphing mode. ♦ qMin, qMax, and qStep are available in Pol graphing mode. The values shown in the picture to the right are the defaults in Radian mode. $ indicates that yMin=L10, yMax=10, and yScl=1 are beyond the screen. qMin=0

Specifies the first q value to evaluate within the graph screen

qMax default is 2p.

qMax=6.28318530718

Specifies the last q value to evaluate within the graph screen

qStep default is pà24.

qStep=.13089969389957

Specifies the increment from one q value to the next q value

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Chapter 8: Polar Graphing

DrawLine graph format

typically displays a more meaningful polar graph than DrawDot graph format.

119

Setting the Graph Format To display the format screen in Pol graphing mode, select FORMT from the GRAPH menu (6 / (). Chapter 5 describes the format settings. Although the same settings are available for Func, Pol, and Param graphing modes, the TI-86 retains in memory separate format settings for each mode. In Pol graphing mode, PolarGC shows the cursor coordinates in terms of r and q, the variables that define the equations. Displaying the Graph To plot the selected polar equations, you can select GRAPH, TRACE, EVAL, RCGDB, or a ZOOM, MATH, DRAW, or RCPIC operation, from the GRAPH menu. The TI-86 evaluates r for each value of q (from qMin to qMax in intervals of qStep) and then plots each point. As the graph is plotted, the variables q, r, x, and y are updated.

Using Graph Tools in Pol Graphing Mode The Free-Moving Cursor The free-moving cursor in Pol graphing works the same as in Func graphing. ♦ In RectGC format, moving the cursor updates the values of x and y; if CoordOn format is selected, x and y are displayed. ♦ In PolarGC format, moving the cursor updates x, y, r, and q; if CoordOn format is selected, r and q are displayed.

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120

Chapter 8: Polar Graphing

Tracing a Polar Equation To begin a trace, select TRACE from the GRAPH menu (press 6 )). The trace cursor appears on the first selected equation at qMin. ♦ In RectGC format, moving the trace cursor updates the values of q, x, and y; if CoordOn format is selected, q, x, and y are displayed. ♦ In PolarGC format, moving the trace cursor updates x, y, r, and q; if CoordOn format is selected, r and q are displayed.

QuickZoom is available in Pol graphing; panning is not (Chapter 6).

To move the trace cursor...

Press:

Along the graph of the equation by increments or decrements of qStep

" or !

From one equation to another

# or $

If you move the trace cursor beyond the top or bottom of the graph screen, the coordinate values at the bottom of the screen continue to change appropriately. If you have graphed a family of curves, # and $ move through each curve before moving to the next polar equation.

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Chapter 8: Polar Graphing

121

Moving the Trace Cursor to a q Value To move the trace cursor to any valid q value on the current equation, enter the number. When you enter the first digit, a q= prompt is displayed in the bottom-left corner. The value you enter must be valid for the current graph screen. When you have completed the entry, press b to reactivate the trace cursor. In the example, r1=8sin(2.5q) is graphed. Values for q, x, and y are displayed on the graph to the right because RectGC graph format is selected.

Using Zoom Operations The GRAPH ZOOM menu items, except ZFIT, work the same in Pol graphing as in Func graphing. In Pol graphing mode, ZFIT adjusts the graph screen in both the x and y directions. The zoom operations affect only the x window variables (xMin, xMax, and Xscl) and the y window variables (yMin, yMax, and yScl), except ZSTO and ZRCL, which also affect the q window variables (qMin, qMax, and qStep).

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122

Chapter 8: Polar Graphing

The GRAPH MATH Menu MATH DIST The other GRAPH MATH menu items are the same as described in Chapter 6.

dràdq

6/&

DRAW FORMT STGDB RCGDB dyàdx dràdq ARC TANLN Finds the numerical derivative (slope) of a function at a point

The distances calculated by DIST and ARC are distances in the rectangular coordinate plane. dyàdx and dràdq are independent of the RectGC or PolarGC format. At a point where the derivative is undefined, TANLN will draw the line, but no result is displayed or stored in Ans. Evaluating an Equation for a Specified q When the trace cursor is not active, the GRAPH menu item EVAL evaluates selected polar equations directly on the graph for a given value of q. eval in a program or from the home screen returns a list of r values. Drawing on a Polar Graph The GRAPH DRAW menu items work the same in Pol graphing as in Func graphing. DRAW instruction coordinates in Pol graphing mode are the x- and y-coordinates of the graph screen. DrInv is not available in Pol graphing mode.

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9

Parametric Graphing TI-86

Preview: Parametric Graphing ......................................... 124 Defining a Parametric Graph ........................................... 125 Using Graph Tools in Param Graphing Mode .................. 128

M1

M2

M3

M4

M5

F1

F2

F3

F4

F5

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124

Chapter 9: Parametric Graphing

Preview: Parametric Graphing Graph the parametric equation that describes the path of a ball kicked at an initial speed of 30 meters per second, at an initial angle of 25 degrees with the horizontal (from ground level). How far does the ball travel? When does it hit the ground? How high does it go?

In the example, ignore all forces except gravity. For initial velocity v0 and angle q, the position of the ball as a function of time has horizontal and vertical components.



Select Param mode from the mode screen.

-m### #""b



Display the equation editor and parametric equation editor menu. Deselect all equations and plots (if any are defined).

6& (/ ' /)



Define the path of the ball as xt1 and yt1 in terms of t. Horizontal: xt1=tv0cos(q) Vertical: yt1=tv0sin(q)N1à2(gt2) Gravity constant: g=9.8 màsec2

30 & > D 25



Define the vertical component vector as xt2 and yt2 and define the horizontal component vector as xt3 and yt3.



Change the graph style of xt3àyt3 to ¼ (thick). Change the graph style of xt2àyt2 and xt1/yt1 to À (path).

-Œ(&E # 30 - e = D 25 & E T 9 ` 8F2-eI # 0#-g1# - f1#0

./)$ $))$$$ ))

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Chapter 9: Parametric Graphing

Enter these window variable values. tMin=0 tMax=5 tStep=.1

To simulate the ball in flight, change the graph style of xt1àyt1 to Á (animate).

xMin=L20 xMax=100 xScl=50

yMin=L5 yMax=15 yScl=10

125

-f0#5# ` 1 # a 20 # 100 # 50 # a 5 # 15 # 10



Set SimulG and AxesOff graphing formats, so the path of the ball and the vectors will be plotted simultaneously on a clear graph screen.

/(### "b##" b



Plot the graph. The plotting action simultaneously shows the ball in flight and the vertical and horizontal component vectors of the motion.

*



Trace the graph to obtain numerical results. Tracing begins at tMin and traces the path of the ball over time. The value displayed for x is distance; y is height; t is time.

)"

Defining a Parametric Graph The steps for defining a parametric graph are similar to the steps for defining a function graph. This chapter assumes that you are familiar with Chapter 5: Function Graphing and Chapter 6: Graph Tools. This chapter details those aspects of parametric graphing that differ from function graphing.

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126

Chapter 9: Parametric Graphing

Setting Parametric Graphing Mode To display the mode screen, press - m. To graph parametric equations, you must select Param graphing mode before you enter equations, set the format, or edit window variable values. The TI-86 retains in memory separate equation, format, and window data for each graphing mode. The GRAPH Menu Chapter 5 describes these GRAPH menu items: GRAPH and FORMT. Chapter 6 describes these GRAPH menu items: ZOOM, TRACE, DRAW, STGDB, RCGDB, EVAL, STPIC, and RCPIC.

A common application of parametric graphs is graphing equations over time.

E(t)=

WIND

parametric parametric equation window editor editor

6 ZOOM

TRACE GRAPH

4

MATH

DRAW FORMT STGDB RCGDB

4

EVAL

STPIC

RCPIC

parametric graph math menu

Displaying the Parametric Equation Editor To display the parametric equation editor, select E(t)= from the GRAPH menu in Param graphing mode (6 &). The equation editor menu displayed on the bottom line is the same as the Func-mode equation editor menu, except that t and xt replace x and y, and yt displaces INSf. In this editor, you can enter and display both the x and y components of up to 99 parametric equations, xt1 and yt1 through xt99 and yt99, if sufficient memory is available. Each is defined in terms of the independent variable t. Two components, x and y, define a single parametric equation. You must define both xt and yt for each equation. The default graph style is » (line) in Param mode. ¾ (shade above) and ¿ (shade below) graph styles are not available in Param mode.

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Chapter 9: Parametric Graphing

127

Selecting and Deselecting a Parametric Equation When a parametric equation is selected, the equals signs (=) of both xt and yt are highlighted. To change the selection status of a parametric equation, move the cursor onto either xt or yt, and then select SELCT from the equation editor menu. The status is changed for xt and yt. Deleting a Parametric Equation To delete a parametric equation using DELf, move the cursor to either xt or yt, and then select DELf from the equation editor menu. Both components are deleted. To delete a parametric equation using the MEM DELET menu (Chapter 17), you must select the xt component. If you select the yt component, the equation is retained in memory. Setting the Graph Screen Window Variables To display the parametric window editor, select WIND from the GRAPH menu (6 '). Param graphing mode has the same window variables as Func graphing mode, except: ♦ xRes is not available in Param mode. ♦ tMin, tMax, and tStep are available in Param mode. The values shown in the picture to the right are the defaults in Radian mode. $ indicates that yMin=L10, yMax=10, and yScl=1 are beyond the screen. tMin=0

Specifies the starting t value

tMax default is 2p.

tMax=6.28318530718

Specifies the ending t value

tStep default is pà24.

tStep=.13089969389957

Specifies the increment from one t value to the next

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128

Chapter 9: Parametric Graphing

DrawLine graph format

typically displays a more meaningful parametric graph than DrawDot graphing format.

Setting the Graph Format To display the format screen in Param graphing mode, select FORMT from the GRAPH menu (6 / (). Chapter 5 describes the format settings. The TI-86 retains in memory separate format settings for Func, Pol, Param , and DifEq graphing modes. Displaying the Graph To plot the selected parametric equations, you can select GRAPH, TRACE, EVAL, RCGDB, or a ZOOM, MATH, DRAW, or RCPIC operation. The TI-86 evaluates x and y for each value of t (from tMin to tMax in intervals of tStep) and then plots each point defined by x and y. As the graph is plotted, the variables x, y, and t are updated.

Using Graph Tools in Param Graphing Mode The Free-Moving Cursor The free-moving cursor in Param graphing works the same as in Func graphing. ♦ In RectGC format, moving the cursor updates the values of x and y.; if CoordOn format is selected, x and y are displayed. ♦ In PolarGC format, moving the cursor updates x, y, r, and q; if CoordOn format is selected, r and q are displayed. Tracing a Parametric Function To begin a trace, select TRACE from the GRAPH menu (6 )). When you begin a trace, the trace cursor is on the first selected function at tMin. ♦ In RectGC format, moving the trace cursor updates the values of x, y, and t; if CoordOn format is selected, t, x, and y and are displayed.

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Chapter 9: Parametric Graphing



QuickZoom is available in Param graphing; panning is not (Chapter 6).

You can enter an expression at the t= prompt.

129

In PolarGC format, moving the trace cursor updates x, y, r, q, and t; if CoordOn format is selected, r, q, and t are displayed. The x and y (or r and q) values are calculated from t.

To move the trace cursor...

Press:

Along the graph of the equation by increments or decrements of tStep

" or !

From one equation to another

# or $

If you move the trace cursor beyond the top or bottom of the graph screen, the coordinate values at the bottom of the screen continue to change appropriately. If you have graphed a family of curves, # and $ move through each curve before moving to the next parametric function. Moving the Trace Cursor to a t Value To move the trace cursor to any valid t value on the current equation, enter the number. When you enter the first digit, a t= prompt is displayed in the bottom-left corner. The value you enter must be valid for the current graph screen. When you have completed the entry, press b to reactivate the trace cursor.

In the example, the parametric equation is: xt1=95t cos 30¡ yt1=95t sin 30¡N16t 2 Also, AxesOn graph format is

set. (The example on page 124 is similar to this example.)

Using Zoom Operations The GRAPH ZOOM menu items, except ZFIT, work the same in Param graphing as in Func graphing. In Param mode, ZFIT adjusts the graph screen in both the x and y directions.

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Chapter 9: Parametric Graphing

The GRAPH ZOOM menu items affect only the x window variables (xMin, xMax, and xScl) and the y window variables (yMin, yMax, and yScl), except ZSTO and ZRCL, which also affect the t window variables (tMin, tMax, and tStep). The GRAPH MATH Menu MATH DIST The other GRAPH MATH menu items are the same as described in Chapter 5.

6/&

DRAW FORMT STGDB RCGDB dyàdx dyàdt dxàdt ARC

4

TANLN

dyàdx

Returns the derivative of yt divided by the derivative of xt

dyàdt

Returns the derivative of the yt equation at a point with respect to t

dxàdt

Returns the derivative of the xt equation at a point with respect to t

The distances calculated by DIST and ARC are distances in the rectangular coordinate plane. At a point where the derivative is undefined, TANLN will draw the line, but no result is displayed or stored in Ans. Evaluating an Equation for a Specified t When the trace cursor is not active, the GRAPH menu item EVAL evaluates selected polar equations directly on the graph for a given value of t. eval in a program or from the home screen returns a list of x and y values in this form: {xt1(t) yt1(t) xt2(t) xt2(t) ...}. Drawing on a Parametric Graph The DRAW menu items work in Param graphing the same as in Func graphing. DRAW instruction coordinates in Param graphing are the x- and y-coordinate values of the graph screen.

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10

Differential Equation Graphing TI-86

Defining a Differential Equation Graph............................ 132 Entering and Solving Differential Equations .................... 139 Using Graph Tools in DifEq Graphing Mode .................... 144

M1

M2

M3

M4

M5

F1

F2

F3

F4

F5

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132

Chapter 10: Differential Equation Graphing

Defining a Differential Equation Graph Chapters 8 and 9 each begin with an example; Chapter 10 has several differential equation examples throughout the chapter.

Most steps for defining a differential equation graph are similar to the steps for defining a function graph. This chapter assumes that you are familiar with Chapter 5: Function Graphing and Chapter 6: Graph Tools. This chapter details aspects of differential equation graphing that differ from function graphing. Generally, DifEq graphing mode differs from other graphing modes in these ways. ♦ You must select the field format or accept the default before defining the equations (page 133). ♦ If an equation is higher than first order, you must convert it to an equivalent system of first-order differential equations, and then store the system in the equation editor (page 140 and page 142). ♦ When FldOff field format is selected, you must set initial conditions for each equation in the system (page 136). ♦ After you have selected the field format setting, you must select AXES from the GRAPH menu and enter axes information or accept the defaults (page 137). Setting Differential Equation Graphing Mode To display the mode screen, press - m. To graph differential equations, you must select DifEq graphing mode before you set the format, enter equations, or edit window variable values. The TI-86 retains in memory separate format, equation, and window data for each graphing mode.

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Chapter 10: Differential Equation Graphing

The GRAPH Menu Chapter 5 describes the GRAPH menu item GRAPH. Chapter 6 describes these GRAPH menu items: DRAW, ZOOM, TRACE, EVAL, STGDB, RCGDB, STPIC, and RCPIC.

The TI-86 retains independent format settings for each graphing mode.

Q'(t)=

WIND

6 INITC

AXES

GRAPH

4 4

equation initial conditions editor editor differential equation axes window editor editor

FORMT DRAW EVAL

ZOOM

TRACE EXPLR

STGDB RCGDB STPIC

RCPIC

explore with the free-moving cursor differential equation format screen

Setting the Graph Format To display the format screen in DifEq graphing mode, select FORMT from the GRAPH menu (6 / &). ♦ The RK Euler and SlpFld DirFld FldOff format settings are available only in DifEq mode. ♦ The RectGC PolarGC, DrawLine DrawDot, and SeqG SimulG format settings are not available in DifEq graphing mode. ♦ All other format settings are the same as described in Chapter 5. Solution Method Format RK

Uses the Runge-Kutta method to solve differential equations more accurately than the Euler solution method format, but not as fast

Euler

Uses the Euler method to solve differential equations; requires a number of iterations between tStep values, so EStep= prompt replaces difTol= prompt on the window editor

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134

Chapter 10: Differential Equation Graphing

Field Format SlpFld

(slope field) Adds the slope field to the graph of only one first-order equation with t on the x-axis and a specified Qn equation on the y-axis

DirFld

(direction field) Adds the direction field to the graph of only one second-order equation with Qx# on the x-axis and Qy# on the y-axis

FldOff

(field off) Graphs all selected differential equations with t or Q1 on the x-axis, Q1 or Q2 on the y-axis, and no field; initial conditions must be defined for all equations (page 136)

The examples below show the basic slope and direction fields; all unspecified settings and values are defaults. To replicate these examples, reset defaults, enter the specified information in DifEq graphing mode, and then press 6 *. Axes information is stored to GDB and PIC variables.

SlpFld field format

DirFld field format

Q'1=t (y'=x)

Q'1=Q2 and Q'2=LQ1 (y"=Ly)

To remove menus from a graph, as shown in the examples, press :.

Displaying the Differential Equation Editor To display the differential equation editor, select Q'(t)= from the GRAPH menu in DifEq graphing mode (6 &). The DifEq equation editor menu on the bottom line is the same as the Func mode equation editor menu, except that t and Q replace x and y.

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Chapter 10: Differential Equation Graphing

135

In this editor, you can enter and display a system of up to nine first-order differential equations, Q'1 through Q'9, if sufficient memory is available. Equations are defined in terms of the independent variable t andàor Q'. You can refer to another differential equation variable in a DifEq equation, as in Q'2=Q1. However, you cannot enter a list in a DifEq equation.

When the TI-86 calculates a differential equation system, it references all equations in the equation editor, regardless of selection status, starting at Q'1. You must define Q'n equation variables consecutively, starting at Q'1. For example, if Q'1 and Q'2 are not defined, but you attempt to solve an equation defined in Q'3, the calculator returns an error. The TI-86 allows you to analyze each equation independently. For example, you can enter Q'1=t and Q'2=t 2 and analyze each equation independently.

The TI-86 graphs only those selected equations that are appropriate for the specified axes. ♦ The default graph style is ¼ (thick) in DifEq mode. ♦ ¾ (shade above), ¿ (shade below), and  (dot) are not available in DifEq graphing mode. Setting the Graph Screen Window Variables To display the differential equation window editor, select WIND from the GRAPH menu (6 '). DifEq has the same window variables as Func graphing mode, except: ♦ xRes is not available in DifEq mode. ♦ tMin, tMax, tStep, and tPlot are available in DifEq mode. ♦ difTol (RK) and EStep (Euler) are available in DifEq mode.

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136

Chapter 10: Differential Equation Graphing

The values shown in the picture on page 135 are defaults in Radian mode. x and y settings correspond to the axes variables (page 137). $ indicates that xScl=1, yMin=L10, yMax=10, yScl=1, and difTol=.001 (in RK format) or EStep=1 (in Euler format) are beyond the screen. tMin=0

Specifies the t value at which to begin evaluating within a graph screen

tMax default is 2p.

tMax=6.28318530718

Specifies the last t value to evaluate within a graph screen

tStep default is pà24.

tStep=.1308969389958

Specifies the increment from one t value to the next t value

tPlot=0

Specifies the point at which plotting begins (ignored when t is an axis)

difTol=.001 (in RK format) Specifies tolerance to help select step size for solving; must be ‚ 1EL12 EStep=1 (in Euler format) Specifies Euler iterations between tStep values; must be an integer >0 and  25

Initial conditions information is stored to GDB and PIC variables.

Setting the Initial Conditions To display the initial conditions editor, select INITC from the GRAPH menu (6 (). On this editor, you can set the initial value at t=tMin for each first-order equation in the equation editor. tMin is the first t value to evaluate. Q[1 is the initial value of Qn. A small square next to an initial condition variable

indicates that a value is required for a defined differential equation. You can enter an expression, list, or list name for initial conditions tMin and Q[n. When you enter a list name, the elements are displayed when you press b, # or $. ♦ If SlpFld or DirFld format is set, you need not specify initial conditions. The TI-86 returns the appropriate field with no specific solutions. ♦ If FldOff format is set, you must specify initial conditions.

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Chapter 10: Differential Equation Graphing

137

Setting the Axes To display the axes editor, select AXES from the GRAPH menu in DifEq mode (6 )). x= assigns a variable to the x-axis dTime= specifies a point in time (real number) y= assigns a variable to the y-axis fldRes= (resolution) sets number of rows (1 through 25) At the x= and y= prompts, you can enter the independent variable t, as well as Q, Q' , Qn, or Q'n, where n is an integer ‚ 1 and  9. If you assign t to one axis and Qn or Q'n to the other axis, only the equation stored to Qn or Q'n is plotted; other differential equations in the equation editor are not plotted; their selection status is ignored. dTime is only valid for second-order equations with t in either equation. The axes editor and defaults for each field format are shown below. When SlpFld field format is set, the x-axis is always t, so the AXES: SlpFld editor does not display x=t. Axes information is stored to GDB and PIC variables.

When SlpFld format is set:

When DirFld format is set:

When FldOff format is set:

Differential Equation Graphing Tips ♦ Since the TI-86 plots slope fields and direction fields before it plots equations, you can press b to pause the graph and view the fields with no solutions plotted. ♦ If you do not specify initial conditions for the equations assigned to the axes, the TI-86 simply draws the field and stops. This gives you access to both the field format options and the interactive initial conditions simultaneously.

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Chapter 10: Differential Equation Graphing

Stat plot and screen drawings are not stored to fldPic.

The Built-In Variable fldPic As the TI-86 plots a field, it stores the field and any displayed label, axes, or cursor coordinate information to the built-in variable fldPic. These actions do not update fldPic. ♦ Switching the solving method format from RK to Euler or from Euler to RK ♦ Entering or editing any initial condition variable value (Q[1 through Q[9) ♦ Editing a value for difTol, EStep, tMin, tMax, tStep, or tPlot ♦ Changing a graph style These actions update fldPic. ♦ Editing an equation in the equation editor ♦ Re-assigning an axis, editing a dTime value, or editing a fldRes value ♦ Using a GRAPH ZOOM menu item ♦ Changing a format setting other than solving method format ♦ Editing a value for xMin, xMax, xScl, yMin, yMax, or yScl Displaying the Graph To plot the differential equations, you can select GRAPH, TRACE, EVAL, or STGDB, or a DRAW, ZOOM, or STPIC operation, from the GRAPH menu. The TI-86 solves each equation from tMin to tMax. If t is not an axis, it plots each point beginning at tPlot; otherwise, it begins at tMin. As a graph is plotted, the variables x, y, t, and Qn are updated. tStep affects trace resolution and graph appearance, but not the accuracy of the trace values. tStep does not determine the step size for solving; using the RK algorithm (RungeKutta 2-3) determines the step size. If the x-axis is t, setting tStep<(tMax N tMin)à126 increases plotting time without increasing accuracy.

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Chapter 10: Differential Equation Graphing

139

Entering and Solving Differential Equations In Func graphing mode, x is the independent variable and y is the equation variable. To avoid conflict between Func equations and DifEq equations on the TI-86, t is the independent variable and Q'n is the equation variable in DifEq graphing mode. Therefore, when you enter an equation in the differential equation editor, you must express it in terms of t and Q'n. For example, to express the first-order differential equation y'=x2, you would substitute t 2 for x 2 and Q'1 for y', and then enter Q'1=t 2 in the equation editor. Graphing in SlpFld Format

In the example, the default window variable values are set initially.



Display the mode screen and set DifEq graphing mode.

-m### #"""b



Display the format screen and set SlpFld field format.

6/&# ####b



Display the equation editor and store the differential equation y'=x2, substituting Q'1 for y' and t for x. Clear any other equations.

&&I



Display the initial conditions editor and enter the initial conditions. A small square indicates that an initial condition is required.

-g3

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Chapter 10: Differential Equation Graphing

In SlpFld field format, x=t is always true; y=Q1 and fldRes=15 are the default axes settings.



Display the axes editor and enter the equation variable for which you want to solve. (Do not set y=Q.)



Accept or change fldRes (resolution).



Display the graph. With the default window variable values set, the slope fields for this graph are not very illustrative.

-i



Change the window variables xMin, xMax, yMin, and yMax.

'####0 # 5 # # 0 # 20



Select TRACE from the GRAPH menu to replot the graph and activate the trace cursor. Trace the solution. The trace cursor coordinates for t and Q1 are displayed.

/)

)&1

" and !

Transforming an Equation into a First-Order System On the TI-86, to enter a second-order or higher (up to ninth-order) differential equation, you must transform it to a system of first-order differential equations. For example, to enter the second-order differential equation y''= L y, you must transform it to two first-order differential equations, as shown in the chart below. Differentiate...

Define the variables as...

And then substitute:

Q'1=y'

Q1=y

Q'1=Q2 (since Q'1=y'=Q2)

Q'2=y''

Q2=y'

Q'2=LQ1

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Chapter 10: Differential Equation Graphing

Graphing in DirFld Format

In DifEq graphing mode, t is the independent variable and Q'n is the dependent variable, where n ‚ 1 and  9.



Display the mode screen and set DifEq graphing mode.

-m### #"""b



Display the format screen and set DirFld graphing format.

6/&# ####"b



Display the equation editor and store the transformed system of differential equations for y''=Ly to the equation editor, substituting Q1 for y and Q2 for y'.

&'2#a'1



Display the initial conditions editor and enter the initial conditions if you want a specific solution. To enter a list of initial conditions, use { and } from the LIST menu.

-g-” & 1P2P5' # & -~ P 4 P 5 ` 75 '



Display the axes editor and enter the two equation variables for which you want to solve. You must omit the prime mark ( ' ).

-h&1# &2



Accept or change fldRes (resolution).



Select ZSTD from the GRAPH ZOOM menu to set the standard window variable values and display the graph.

In the example, the default window variable values are set initially.

When DirFld field format is selected, x=Q1, y=Q2, dTime=0, and fldRes=15 are the default axes settings. Since t is not part of the equation, dTime is ignored.

Clear the GRAPH menu from the screen.

./()

:

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141

142

Chapter 10: Differential Equation Graphing

Graphing a System of Equations in FldOff Format For this example, you must transform the fourth-order differential equation y (4)Ny=e Lx into an equivalent system of first-order differential equations, as shown in the chart below. Differentiate...

Define the variables as...

And then substitute:

Q'1=y'

t=x Q1=y

Q'1=Q2 (since Q'1=y'=Q2)

Q'2=y''

Q2=y'

Q'2=Q3

Q'3=y'''

Q3=y''

Q'3=Q4

Q4=y'''

Q'4=e Lt+Q1 (since Q'4=y (4)=e Lx+y=e Lt+Q1)

Q'4=y

In DifEq graphing mode, t is the independent variable and Q'n is the equation variable, where n ‚ 1 and  9.

(4)



Display the mode screen and set DifEq graphing mode.

-m### #"""b



Display the format screen and set FldOff field format.

6/&# ####"" b



Display the equation editor and store the transformed system of differential equations for y (4)=eLx+y, substituting as shown in the chart.

&'2#'3# '4#- ‚D a&E\ '1



Deselect Q'3, Q'2, and Q'1 to plot Q'4=e^(Lt)+Q1 only.

$*$*$*

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Chapter 10: Differential Equation Graphing

When FldOff field format is selected, x=t and y=Q are the default axes settings.



Display the window editor and set the window variable values.

- f # 10 # ` 01 # # 0 # ##a4#4



Display the initial conditions editor and enter the initial conditions. A small square indicates that an initial condition is required.

( 3 # a 5 ` 25 #7`5# a 5 ` 75



Display the axes editor. Enter the equation variables for which you want to solve.

)



Display the graph. Explore the equation with the trace cursor.

./) " and !



Enter a t value to move the trace cursor to the solution for that t value. The t and Q4 coordinates are displayed.

4b

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143

144

Chapter 10: Differential Equation Graphing

To paste ' to the home screen, you can select it from the CHAR MISC menu or from the CATALOG. Due to TI-86 system requirements, you must express Q1(3) as Q'1(3) on the calculator.

Solving a Differential Equation for a Specified Value On the home screen in DifEq graphing mode, you can solve a differential equation stored to a specified independent variable value or expression. The syntax is: Q'n(value). ♦ The equation must be stored to a DifEq equation variable (Q'1 through Q'9). ♦ The initial conditions must be defined. ♦ The result sometimes varies, depending on the axes settings.

Using Graph Tools in DifEq Graphing Mode The Free-Moving Cursor The free-moving cursor works in DifEq mode as it does in Func graphing. The cursor coordinate values for x and y are displayed, and the variables are updated. Tracing a Differential Equation To begin a trace, select TRACE from the GRAPH menu (6 / )). The trace cursor appears on the first equation at or near tPlot (or tMin, if t is an axis). The trace coordinates displayed at the bottom of the screen reflect the axes settings. For example, if x=t and y=Q1, then t and Q1 are displayed. If t is not an axis, three trace values are displayed. If t is an axis, only t and the variable designated as the y-axis are displayed. QuickZoom is available in DifEq graphing; panning is

not (Chapter 6).

The trace cursor moves in increments or decrements of tStep. As you trace an equation, the coordinates are updated and displayed. If the cursor moves off the screen, the coordinate values displayed at the bottom of the screen continue to change appropriately.

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Chapter 10: Differential Equation Graphing

145

Moving the Trace Cursor to a t Value To move the trace cursor to any valid t value on the current equation, enter the number. When you enter the first digit, a t= prompt is displayed in the bottom-left corner. The value you enter must be valid for the current graph screen. When you have completed the entry, press b to reactivate the trace cursor. Values for t and Q are displayed on the graph to the right because x=t and y=Q graph axes are selected.

Drawing on a Differential Equation Graph The GRAPH DRAW menu items work the same in DifEq graphing mode as in Func graphing. DRAW instruction coordinates are the x- and y-coordinates of the graph screen. DrEqu is available only in DifEq mode. DrInv is not available in DifEq graphing mode.

Drawing an Equation and Storing Solutions to Lists To draw a solution on the current graph screen and store the results to specified list names, the syntax is: DrEqu(xAxisVariable,yAxisVariableã,xList,yList,tListä) xAxisVariable and yAxisVariable specify the axes on which the drawing is based; they may differ from the current graph screen’s axes settings.

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Chapter 10: Differential Equation Graphing

DrEqu( does not store values to x, y, or t.

xList, yList, and tList are optional list names to which you can store the solutions x, y, and t. You then can display the lists on the home screen or in the list editor (Chapter 11). Use the free-moving cursor to select initial conditions. You cannot trace the drawing. However, you can plot xList, yList, or tList as a stat plot after you draw the equation, and then trace them (Chapter 14). Also, you can fit statistical regression models to the lists (Chapter 14).

In the example, the default window variable values are set. If necessary, select ZSTD from the GRAPH ZOOM menu.



Display the mode screen and set DifEq graphing mode.

-m### #"""b



Display the format screen and set DirFld field format.

6/&# ####" b

If you select FldOff field format, you must enter initial conditions before you use DrEqu(.



Display the equation editor and store the equations Q'1=Q2 and Q'2=LQ1. (Delete all other equations.)

&'2#a'1



Remove the format screen, and then select DrEqu from the GRAPH DRAW menu. DrEqu( is pasted to the home screen.

..6 /'&



Assign variables to the x- and y-axes.

1 ãQä 1 P 1 ãQä 2 P



Specify list names to which to store the solution lists for x, y, and t.

1 ãLä 1 ãXä P 1 ãLä 1 ãYä P 1 ãLä 1 ãTä E

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Chapter 10: Differential Equation Graphing In the example, since no initial conditions were set, the equation in Q'1 is not plotted.



Display the graph screen and plot the direction field.

b



Move the free-moving cursor to the initial condition coordinates you want.

"#!$



147

Draw the solution. The solution lists for b x, y, and t are stored to LX, LY, and LT. The Again? prompt is displayed and ALPHA-lock is on for ãYä and ãNä only. ♦ To use DrEqu( again with new initial conditions, press ãYä, ", #, !, or $. ♦ To leave DrEqu( and display the GRAPH menu, press ãNä or ..

Using ZOOM Operations The GRAPH ZOOM menu items, except ZFIT, work the same in DifEq graphing mode as in Func graphing mode. In DifEq graphing mode, ZFIT adjusts the graph screen in both the x direction and y direction. The ZOOM menu items affect only the x (xMin, xMax, and xScl) and y (yMin, yMax, and yScl) window variables. The t window variables (tMin, tMax, tStep, and tPlot) are not affected, except with ZSTD and ZRCL. You may want to edit the t window variables to ensure that sufficient points are plotted. ZSTD sets difTol=.001 and t and Q as the axes.

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Chapter 10: Differential Equation Graphing

Drawing Solutions Interactively with EXPLR

Display the mode screen and set DifEq graphing mode.

-m### #"""b



Display the format screen and set FldOff field format.

6/&# ####"" b



Display the equation editor and store the equation Q'1=.001Q1(100NQ1). (Delete all other equations.)

& ` 001 ' 1 D 100 T ' 1 E



Set the axes to x=t and y=Q1.

-h#"1



Display the window editor and set the window variable values.

- f # 100 # `2### 100 # # # 110



Display the initial conditions editor and enter the initial condition.

( 10

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Chapter 10: Differential Equation Graphing

Select EXPLR from the GRAPH menu.

/*



Move the free-moving cursor to the initial condition for which you want to solve.

"#!$



Draw the solution to Q1, using the cursor coordinates (x,y) as initial condition ( t,Q'1(t) ).

149

b

To continue drawing more solutions, move the free-moving cursor and then press b. To stop using EXPLR, press .. If SlpFld or DirFld is set, the axes are set to specific solutions automatically. ♦ For SlpFld, x=t and y=Q1 are set. ♦ For DirFld, x=Q1 and y=Q2 are set. If the axes are set to a specific solution t, Qn, or Q'n, that solution is drawn. If the axes are not set to a specific solution and t is one variable and Q is the other, Q1 is drawn. If both axes are set to a Q variable, executing EXPLR results in an error.

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Chapter 10: Differential Equation Graphing

Evaluating Differential Equations for a Specified t When the trace cursor is not active, the GRAPH menu item EVAL evaluates currently selected differential equations Qn for a specified value of t, tMinttMax. You can use it directly on the graph. In a program or from the home screen, eval returns a list of Q values. When DirFld or SlpFld field format is set, you must specify initial conditions before using EVAL.

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11

Lists TI-86

Lists on the TI-86............................................................. 152 Creating, Storing, and Displaying Lists ............................ 153 The List Editor .................................................................. 156 Using List Operations....................................................... 159 Using Mathematical Functions with Lists ........................ 161 Attaching a Formula to a List Name ................................ 162

M1

M2

M3

M4

M5

F1

F2

F3

F4

F5

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Chapter 11: Lists

Lists on the TI-86 The length and number of lists you can store in the TI-86 is limited only by memory capacity.

A list is a set of real or complex elements, as in {5,L20,13,9}. On the TI-86, you can: ♦ Enter a list directly in an expression (page 153) ♦ Enter a list and store it to a list name (variable) (page 154) ♦ Enter a list name in the list editor (page 156), and then enter elements directly or use an attached formula to generate them automatically (page 161) ♦ Collect data with the Calculator-Based Laboratory™ (CBL 2™/CBL™) or Calculator-Based Ranger™ (CBR) and store it to a list name on the TI-86 (Chapter 18) ♦ Create lists dynamically using the LIST OPS menu item seq (page 159)

If you enter more than one list in an equation or expression, all lists must have the same number of elements.

On the TI-86, you can use a list: ♦ As a set of values for an argument in a function to return a list of answers (Chapter 1) ♦ As part of an equation to graph a family of curves (Chapter 5) ♦ As a set of statistical data to analyze with statistical functions and plot on the graph screen (Chapter 14) The LIST Menu {

}

open brace close brace

-” NAMES list names menu

EDIT

OPS

list operations menu list editor

When you enter a list, { (open brace) specifies the beginning and } (close brace) specifies the end. To paste { or } to the cursor location, select either from the LIST menu.

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Chapter 11: Lists

The LIST NAMES Menu The LIST NAMES menu shown here has no usercreated list names. Chapter 14 describes fStat, xStat, and yStat.

{ fStat

} xStat

NAMES yStat

-”( EDIT

OPS

Each user-created list name is added to the LIST NAMES menu and VARS LIST screen. List names, including fStat, xStat, and yStat, are sorted in alphanumeric order in both places.

Creating, Storing, and Displaying Lists Entering a List Directly in an Expression To enter a list directly, the syntax is: {element1,element2,...,element n}

An ellipsis (...) indicates that a list continues beyond the screen. Use " and ! to scroll the list.

153



Enter any part of the expression that precedes the list.

5M



Select { from the LIST menu to begin the list.

-”&



Enter each list element, separating each from the other with a comma. Each list element can be an expression.

a 16 P 4 P 4IP3 -~



Select } from the LIST menu to end the list.

'



Enter any part of the expression that follows the list.

F4



Evaluate the expression. Any elements that are expressions are evaluated first.

b

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Chapter 11: Lists

Creating a List Name by Storing a List To store a list, the syntax is: {element1,element2, ... ,element n}¶listName You need not enter the close brace ( } ) when you use X to store a list name.

To delete a list name from memory, use the MEM DELETE:LIST screen (Chapter 17).



Enter a list directly. (To store a result expressed as a list and currently stored in Ans, as shown in the example, begin these steps at step 2.)

(steps 2 through 5 above)



Paste ¶ to the cursor location. ALPHA-lock is on.

X

Enter the list name. Either select a name from the

ãAä ãBä ãCä 1123



LIST NAMES menu or directly enter a name one to

eight characters long, starting with a letter.

Store the list to the list name. b

Displaying List Elements Stored to a List Name The TI-86 distinguishes between uppercase and lowercase letters in list names. For example, ABC123, Abc123, and abc123 are three different list names.



Enter the list name on the home screen; either select it from the LIST NAMES menu or enter the characters.

-”( &



Display the list elements.

b

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Chapter 11: Lists

155

Displaying or Using a Single List Element To display or use a single list element, the syntax is: listName(element#) listName(element#) is valid as part of an expression.



Enter the list name; either select it from the LIST NAMES menu or enter the characters.

-”( &

element# is ‚ 1 and  the dimension of the list.



In parentheses, enter the element’s place number in the list.

D4E



Display the list element.

b

value can be an expression.

Storing a New Value to a List Element To store a value to a current element or one element beyond the end of a list, the syntax is: value¶listName(element#)

Enter the value to be stored in a current list element or one element beyond the end.



Paste ¶ to the cursor location.

X



Enter the list name; either select it from the LIST NAMES menu or enter the characters. Enter the element’s place number in parentheses. (In the example, 5 is one beyond the current dimension of ABC123).

&





Enter the new value to the element number. (‡18 is evaluated and added as the fifth element.)

- ˆ 18

1D5E

b

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156

Chapter 11: Lists

Complex List Elements A complex number can be a list element. If at least one list element is a complex number, all elements in the list are displayed as complex. (‡L4 results in a complex number.)

-”)

The List Editor

The list editor is a table where you can store, edit, and view up to 20 lists that are in memory. Also, you can create list names and attach formulas to lists in the list editor. You also can press - š ' to display the list editor. The list editor abbreviates list names and element values when necessary. The entry line displays entire list names and element values.

Current column number List names Table of elements Entry line with current column list name and element number List editor menu

The List Editor Menu { The list editor menu items {, }, NAMES, and OPS are identical to the LIST menu

items (page 152).

}

-”)

NAMES

"

OPS

4

4REAL

"

Designates the beginning and end of a formula to be attached to a list name

4REAL

Converts the current list to a list of real numbers

To use LIST OPS menu items (or any other functions or instructions) in the list editor, the cursor location must be appropriate for the result. For example, you can use the LIST OPS menu item sortA when a list name is highlighted but not when an element is highlighted.

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Chapter 11: Lists

Creating a List Name in the Unnamed Column After memory is reset, xStat, yStat, and fStat are stored to columns 1, 2, and 3. Resetting defaults does not affect the list editor.



Display the list editor.

-”)



Move the cursor to the unnamed column (column 4). The Name= prompt is displayed in the entry line. ALPHA-lock is on.

$"""

To move from the list name in column 1 to the unnamed column, press ! ".



Enter the list name. The list name is displayed at the top of the current column. In the entry line, a list name prompt is displayed. The name becomes a LIST NAMES menu item and a VARS LIST screen item.

ãXä ãYä ãZä b

Inserting a List Name into the List Editor If all 20 columns have list names, you must remove a list name to make room for the unnamed column. To cancel the list name insertion, press :. If a formula were attached to ABC123, the formula would be displayed in the entry line instead of the list shown in step 3 (page 162.)



Move the cursor to column 3.

!



Insert a new, unnamed column. List names shift right, clearing column 3. The Name= prompt and LIST NAMES menu are displayed.

-p



Select ABC12 from the LIST NAMES menu to insert the list name ABC123 into column 3. Elements stored to ABC123 fill the column 3 table of elements. The full value of all ABC123 elements is displayed in the entry line.

&b

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157

158

Chapter 11: Lists

Displaying and Editing a List Element To cancel any editing and restore the original element at the cursor, press : b.



Move the cursor onto the fifth element of ABC123. In the entry line, the list name, the element number in parentheses, and the element’s full value are displayed.

#####

You can enter an expression as an element.



Switch to edit-element context and edit the element in the entry line.

5MD6-~E F4



Enter the edited element. Any expression is evaluated and the value is stored to the current element.

b (or # or $)

Deleting Elements from a List To delete a single element from a list, move the cursor onto the element and press 3. The element is deleted. You can clear all elements from a list in any of three ways. ♦ In the list editor, press $ to move the cursor onto a list name and press : b. ♦ In the list editor, move the cursor onto each element, and then press 3 one by one. ♦ On the home screen or in the program editor, enter 0¶dimL listName to set the dimension of listName to 0 (A to Z Reference). Removing a List from the List Editor To remove a list from the list editor, move the cursor onto the list name and then press 3. The list is not deleted from memory; it is only removed from the list editor.

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Chapter 11: Lists

You can remove all user-created lists from the list editor and restore list names xStat, yStat, and fStat to columns 1, 2, and 3 in either of two ways. ♦ Use SetLEdit with no arguments (page 161). ♦ Reset all memory (Chapter 17). Resetting defaults does not affect the list editor.

Using List Operations The LIST OPS (Operations) Menu { dimL

} sortA

NAMES sortD

EDIT min

-”* OPS max

4

sum

prod

seq

li4vc

vc4li

4

Fill

aug

cSum

Deltal

Sortx

4

Sorty

Select

SetLE

Form

For all LIST OPS menu items except Fill( and sometimes dimL, a directly entered list ({element1,element2,...}) is valid for the list argument.

dimL list

Returns the dimension of (or number of elements in) list

#ofElements ¶dimL listName

Creates listName as a list that is #ofElements in length; each element is a 0

#ofElements¶dimL listName

Redimensions an existing listName; previously entered elements within the new dimension remain; each new list element is a 0; each element in the old list that is outside the new dimension is deleted

SortA and SortD sort

sortA list

Sorts list elements in ascending order, from low to high values

sortD list

Sorts list elements in descending order, from high to low values

complex lists based on magnitude (modulus).

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Chapter 11: Lists

For a complex list, min or max returns the smallest or largest magnitude (modulus).

Selecting Deltal from the menu pastes Deltalst( to the cursor location.

min(list)

Returns the smallest element of a real or complex list

max(list)

Returns the largest element of a real or complex list

sum list

Returns the sum of all the elements of a real or complex list, adding from the last element to the first

prod list

Returns the product of all the elements of a real or complex list

seq(expression,variable, begin,endã,stepä)

Returns a list in which each element is the result of the evaluation of expression with regard to variable for the values ranging from begin to end in intervals of step (step can be negative)

li4vc list li4vc {element1,element2,...}

Converts a real or complex list to a vector

vc4li vector vc4li ãelement1,element2,...ä

Converts a real or complex vector to a list

Fill(number,listName) aug(listA,listB)

Stores a real or complex number to every element of listName (augment) Concatenates the real or complex elements of listA and listB

cSum(list)

Returns a list of the cumulative sums of real or complex list elements, starting with the first element and proceeding to the last

Deltalst(list)

Returns a list containing the differences between consecutive elements for all elements in a real or complex list

Sortx ãListName,ListName,

In ascending order of x elements, sorts xListName , sorts x and y data pairs, and optionally, their frequencies, in xListName, yListName , and frequencyListName; xStat and yStat are defaults

frequencyListNameä For Sortx and Sorty, both lists must have the same number of elements.

Sorty ãxListName,ListName,

frequencyListNameä

In ascending order of y elements, sorts xListName , sorts x and y data pairs, and optionally, their frequencies, in xListName, yListName , and frequencyListName; xStat and yStat are defaults

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Chapter 11: Lists

Selecting SetLE from the menu pastes SetLEdit to the cursor location. You can create new list names as SetLEdit arguments.

161

Select(xListName, yListName)

Selects one or more specific data points from a scatter plot or xyLine plot (only), then stores the selected data points to xListName and yListName (Chapter 14)

SetLEdit ãcolumn1ListName, column2ListName,...,

Sets up the list editor; SetLEdit with one to 20 ListNames loads them in the specified order; SetLEdit with no arguments removes all current list names from the list editor and enters the default lists xStat, yStat, and fStat to columns 1, 2, and 3

column20ListNameä Form("formula",listName)

Attaches formula to listName; formula resolves to a list, which is dynamically stored and updated in listName (page 162)

Using Mathematical Functions with Lists You can use a list as a single argument for many TI-86 functions; the result is a list. The function must be valid for every element in the list; however, when graphing, undefined points do not result in an error. When you use lists for two or more arguments in the same function, all lists must have the same number of elements (equal dimension). Here are some examples of a list as a single argument. {1,2,3}+10 returns {11 12 13}

‡{4,16,36,64} returns {2 4 6 8}

{5,10,15}¹{2,4,6} returns {10 40 90}

sin {7,5} returns {.656986598719 L.958924274663}

3+{1,7,(2,1)} returns {(4,0) (10,0) (5,1)}

{1,15,36}<19 returns {1 1 0}

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Chapter 11: Lists

Attaching a Formula to a List Name You cannot edit an element of a list created from an attached formula unless you first detach the formula from the list name. When you include more than one list name in an attached formula, each list must have the same dimension.

You can attach a formula to a list name so that the formula generates a list that is stored and dynamically updated in the list name. ♦ When you edit an element of a list that is referenced in the formula, the corresponding element in the list to which the formula is attached is updated. ♦ When you edit the formula itself, all elements in the list to which the formula is attached are updated. To attach a formula to a list name on the home screen or in the program editor, the syntax is: Form("formula",listName) When you enter a new list name as the second argument for Form( , the list name is created and stored in the LIST NAMES menu and VARS LIST screen upon execution.

Begin these steps on a blank line on the home screen.

To view a formula attached to a list name, use the list editor (page 157).



Store elements to a list name.

-”&1P2P 3 ' X ãLä 1 1b



Select Form from the LIST OPS menu; Form( is pasted to the cursor location.

*/// )



Enter a formula in quotation marks.

-“&1 ãLä 1 \ 10 &



Enter a comma and then the list name to which you want to attach the formula.

P 1 1 ãAä ãDä ãDä 1 10 E



Attach the formula to the list name.

b

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Chapter 11: Lists

163

Comparing an Attached List with a Regular List To see the differences between an attached list and a regular list, follow these steps. The example below builds on the example above for attaching a formula to a list. Notice that the formula in step 1 below is not attached to LX because it is not set off by quotation marks.

If other list names are stored on the LIST NAMES menu, pressing & and ( may not paste ADD10 and LX to the home screen as shown.



Generate a regular list by storing the expression L1+10 to the list name LX.

1 ãLä 1 \ 10 X ãLä ãXä b



Change the second element in L1 to L8 and display the edited list.

a 8 X ãLä 11D2E -1 ãLä 1 b



Compare the elements of the regular list LX with ADD10, to which the formula L1+10 is attached. Notice that element 2 of LX is unchanged. Meanwhile, element 2 of ADD10 has been recalculated, since element 2 of L1 has been edited.

-”( 'b) b

Using the List Editor to Attach a Formula In the example, only fStat, xStat, and yStat are on the LIST NAMES menu and xStat={L2,9,6,1,L7}.



Display the list editor.

-”)



Highlight the list name to which you want to attach the formula.

$"

The attached formula must be set off by quotation marks.



Enter the formula in quotation marks.

)4M(' -)

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164

Chapter 11: Lists

The list editor displays a formula-lock symbol next to each list name that has a formula attached to it.



Attach the formula and generate the list. The TI-86 calculates each list element. A lock symbol is displayed next to the list name to which the formula is attached.

b

♦ ♦

To edit an attached formula, press b in step 3, and then edit the formula. Using the List Editor With Attached-Formula Lists When you edit an element of a list referenced in an attached formula, the TI-86 updates the corresponding element in the list to which the formula is attached. When you edit or enter elements of a displayed list in any of the three current list editor columns while an attached-formula list also is displayed, the TI-86 takes slightly longer to execute the edit or entry. To reduce this effect, move lists with formulas off the current threecolumn display, either by scrolling columns to the left or right or by rearranging the list editor. Executing and Displaying Attached Formulas An attached formula must resolve to a list upon execution. Some examples of formulas that resolve to a list are "5¹xStat", "seq(x,x,1,10)", and "{3,5, L8,4}2à10". Execution of the formula occurs when you attempt to display the list to which the formula is attached. Also, the formula is executed whenever a list referenced by the formula is modified — whether on the home screen, in the list editor, or in a program.

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Chapter 11: Lists

165

You can successfully attach to a list a formula that does not yet resolve to a list. For example, you can attach "5¹xStat" to the list name BY5 with no elements stored to xStat. However, if you attempt to display BY5 when xStat has no elements, an error occurs. When you attach such a formula to a list name in the list editor, the formula is successfully attached, but an error occurs. This is because the list editor attempts to execute the formula immediately after attaching it to the list name. To view the list editor again, you must return to the home screen and either enter something to cause the formula to resolve to a list or remove the attached-formula list from the list editor using the LIST OPS menu item SetLE (page 161).

All elements of a list referenced by an attached formula must be valid for the attached formula.

Handling Errors Related to Attached Formulas On the home screen, you can attach to a list a formula that references another list that has no elements (dimension is 0; page 161). However, you cannot display the attached-formula list in the list editor or on the home screen until you enter at least one element to the list that the formula references. Tip: If an error menu is returned when you attempt to display an attached-formula list in the list editor, you can select GOTO, write down the formula that is attached to the list name, and then press : b to detach (clear) the formula. Then you can use the list editor to find the source of the error. After making the appropriate changes, you can reattach the formula to the list name. If you do not want to clear the formula, you can select QUIT, display the referenced list on the home screen, and find and edit the source of the error. To edit an element of a list on the home screen, store the new value to listName(element#) (page 155).

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Chapter 11: Lists

Detaching a Formula from a List Name You can detach a formula in any of five ways. ♦ Use dimL to change the dimension of the list (page 159). ♦ Use value¶listName(element#) to store value to an attached-formula list element. ♦ Use ""¶listName, where listName is the attached-formula list. ♦ In the list editor, move the cursor onto the name of the attached-formula list, and then press b : b. All list elements remain, but the formula is detached and the lock symbol disappears. ♦ In the list editor, move the cursor onto an element of the attached-formula list. Press b, edit the element, and then press b. The element changes, the formula is detached, and the lock symbol disappears. All other list elements remain. Editing an Element of a Attached-Formula List As described above, one way to detach a formula from a list name is to edit an element of the attached-formula list. The TI-86 protects against inadvertently detaching the formula from the list name when you move the cursor onto one of the elements. Because of the protection feature, you must press b before you can edit an element of an attached-formula list. The protection feature prevents you from deleting an element of an attached-formula list. To delete an element of a attached-formula list, you must first detach the formula in any of the ways described above.

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12

Vectors TI-86

Vectors on the TI-86 ........................................................ 168 Creating, Storing, and Displaying Vectors........................ 169 Using Mathematical Functions with Vectors.................... 176

M1

M2

M3

M4

M5

F1

F2

F3

F4

F5

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Chapter 12: Vectors

Vectors on the TI-86 A vector is a one-dimensional array, arranged in either one row or one column. The vector elements can be real or complex. You can create, display, and edit vectors on the home screen or in the vector editor. When you create a vector, the elements are stored to the vector name. The TI-86 vector editor displays a vector vertically. On the home screen, a vector is entered and displayed horizontally. When you use a vector in an expression, the TI-86 automatically interprets the vector in the form (row vector or column vector) that is appropriate for the expression. For example, a column vector is appropriate for the expression matrix¹vector. On the TI-86, you can store up to 255 elements to a vector in rectangular form. You can use two- or three-element vectors to define magnitude and direction in a two- or threedimensional space. You can express two- or three-element vectors in different forms, depending on the type of vector. To express a...

You enter:

And the TI-86 returns:

Two-element rectangular vector

ãx,yä

ãx yä

Two-element cylindrical vector

ãr±qä

ãr±qä

Two-element spherical vector

ãr±qä

ãr±qä

Three-element rectangular vector

ãx,y,zä

ãx y zä

Three-element cylindrical vector

ãr±q,zä

ãr±q zä

Three-element spherical vector

ãr±q±fä

ãr±q±fä

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Chapter 12: Vectors

169

Creating, Storing, and Displaying Vectors The VECTR (Vector) Menu NAMES

EDIT

vector names menu

MATH vector math menu

vector editor

-Š OPS

CPLX complex vector menu

vector operations menu

The VECTR NAMES Menu - Š & The VECTR NAMES menu contains all currently stored vector names in alphanumeric order. To paste a vector name to the current cursor location, select it from the menu. Creating a Vector in the Vector Editor The TI-86 distinguishes between uppercase and lowercase letters in vector names. For example, VECT1, Vect1, and vect1 are three different vector names.

$ or # in the first column

indicates additional vector elements.

-Š'



Display the vector Name= prompt screen.

-Š'



ALPHA-lock is on. The VECTR NAMES menu is displayed. Enter a name from one to eight characters long, starting with a letter.

ãVä ãEä ãCä ãTä 11



Display the vector editor. The vector editor menu also is displayed.

b



Accept or change the vector elements dimension with an integer ‚ 1 and  255. The vector is displayed; all elements are 0.

5b

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Chapter 12: Vectors

You can enter an expression at a vector element prompt.



Enter each vector element value at each vector element prompt. You can enter expressions. To move to the next prompt, press b or #. The vector elements are stored to VECT1, which becomes a VECTR NAMES menu item.

The Vector Editor Menu INSi

DELi

a 5 # 49 # 2 ` 45 # ` 89 # 1 ` 8

- Š ' vectorNameb

4REAL

INSi

Inserts a blank element (en=) prompt at the cursor location; shifts current elements down

DELi

Deletes the element from the cursor location and from the vector; shifts elements up

4REAL

Converts the displayed complex number vector to a real number vector

Creating a Vector on the Home Screen

To delete a vector name from memory, use the MEM DELETE:VECTR screen (Chapter 17).

Define the beginning of the vector with ã.

-„

Enter each vector element, separating each from the next with a comma.

5P3P9

Define the end of the vector with ä.

-…



X - n ãVä ãEä ãCä ãTä 1 11b

Store the vector to a vector name from one to eight characters long, starting with a letter. The vector is displayed horizontally and the vector name becomes a VECTR NAMES menu item.

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Chapter 12: Vectors

171

Creating a Complex Vector If any element of a vector is complex, all elements of the vector are displayed as complex. For example, when you enter the vector ã1,2,(3,1)ä , the TI-86 displays ã(1,0) (2,0) (3,1)ä. To create a complex vector from two real vectors, the syntax is: realVector+(0,1)imaginaryVector¶complexVectorName realVector contains the real part of each element and imaginaryVector contains the imaginary part. Displaying a Vector To display a vector, paste the vector name to the home screen, and then press b. To display a specific element of vectorName on the home screen or in a program, the syntax is: vectorName(element#) Real two- and three-element vector results are displayed according to the current vector mode setting: RectV, CylV, or SphereV (Chapter 1). You can select a vector conversion instruction from the VECTR OPS menu to override the mode setting (page 173). Complex vectors are displayed in rectangular form only.

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Chapter 12: Vectors

When you execute the expression, the answer is displayed as a vector.

Using a Vector in an Expression ♦ You can enter the vector directly (for example, 35Nã5,10,15ä). ♦ You can use 1 and - n to enter a vector name’s individual characters. ♦ You can select the vector name from the VECTR NAMES menu (- Š &). ♦ You can select the vector name from the VARS VECTR screen (- w / &). Editing Vector Dimension and Elements

Display the vector Name= prompt screen.

-Š'

Enter the vector name. Either select it from the

&

VECTR NAMES menu or enter the characters.

You can use :, 3, and - p to edit matrix elements. You also can overwrite existing characters.



Display the vector editor.

b



Change or accept the vector dimension.

6b



Move the cursor to any element and edit it. Continue moving the cursor to other elements.

# # # 22 # # 13



Save the changes and exit the vector editor.

.

To use X to change an element value on the home screen, the syntax is: value¶vectorName(element#)

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Chapter 12: Vectors

The VECTR MATH Menu NAMES cross

EDIT unitV

173

-Š(

MATH norm

OPS dot

CPLX

cross(vectorA,vectorB) Returns the cross product of vectorA and vectorB, both of which are real or

complex two-element or three-element vectors; expressed with variables, cross(ãa,b,cä,ãd,e,fä) returns ãbfNce cdNaf aeNbdä unitV vector

Returns a unit vector where each element of a real or complex vector is divided by the vector norm

norm vector

Returns the Frobenius norm ( G(real 2+imaginary 2)) where the sum is over all elements of a real or complex vector

dot(vectorA,vectorB)

Returns the dot product of vectorA and vectorB, both of which are real or complex vectors; expressed with variables, dot(ãa,b,cä,ãd,e,fä) returns ad+be+cf

The VECTR OPS (Operations) Menu NAMES dim Press X to enter the ¶ symbol after #ofElements.

EDIT Fill

MATH 4Pol

OPS 4Cyl

-Š) CPLX 4Sph

4

4Rec

li4vc

vc4li

dim vector

Returns the dimension of (or number of elements in) vector

#ofElements¶dimvectorName

Creates a new vectorName of the specified length (#ofElements); each element is 0

#ofElements¶dimvectorName

Redimensions vectorName to the specified length (#ofElements)

Fill(number,vectorName)

Stores a real or complex number to every element in vectorName

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Chapter 12: Vectors

For the conversion functions below, the three-element vector conversion equations for cylindrical form ãr q zä are: x = r cosq y = r sinq z=z The three-element vector conversion equations for spherical form ãr q fä are: x = r cosq sinf y = r sinq sinf z = r cosf

Complex elements are valid only for li4vc and vc4li.

vector4Pol

Displays a 2-element vector in polar form ãr±qä

vector4Cyl

Displays a 2- or 3-element vector as a cylindrical vector ãr±q 0ä or ãr±q zä

vector4Sph

Displays a 2- or 3-element vector as a spherical vector ãr±q 0ä or ãr±q fä

complexVector4Rec

Displays a 2- or 3-element complexVector in rectangular form ãx yä or ãx y zä

li4vc list

Converts a real or complex list into a vector

vc4li vector

Converts a real or complex vector into a list

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Chapter 12: Vectors

The VECTR CPLX (Complex) Menu NAMES conj

EDIT real

MATH imag

OPS abs

175

-Š* CPLX angle

conj complexVector

Returns a vector in which each element is the complex conjugate of the corresponding element of a complexVector

real complexVector

Returns a real vector in which each element is the real portion of the corresponding element of a complexVector

imag complexVector

Returns a real vector in which each element is the imaginary portion of the corresponding element of a complexVector

abs Vector

Returns a real vector in which each element is either the absolute value of the corresponding element of a real vector or the magnitude (modulus) of the corresponding element of a complexVector

angle complexVector Returns a real vector in which each element is either 0 if the element of

complexVector is real or the polar angle if the element of complexVector is complex; polar angles are calculated as tanL1(complexàreal) adjusted by +p in the second quadrant and by Lp in the third quadrant

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176

Chapter 12: Vectors

Using Mathematical Functions with Vectors To add or subtract two vectors, the dimension of vectorA must equal the dimension of vectorB.

vectorA+vectorB

Adds each vectorA element to the corresponding vectorB element; returns a vector of the sums

vectorANvectorB

Subtracts each vectorB element from the corresponding vectorA element; returns a vector of the differences

You cannot multiply two vectors or divide one vector by another vector.

vector¹number or number¹vector

Returns a vector that is the product of a real or complex number times each element in a real or complex vector

matrix¹vector

Returns a vector that is the product of each vector element times each matrix element; matrix column dimension and vector dimension must be equal

vectorànumber

Returns a vector that is the quotient of each real or complex vector element divided by a real or complex number

Mvector

(negation) Changes the sign of each vector element

vectorA==vectorB

Returns 1 if every corresponding element comparison is true; returns 0 if any is false

vectorAƒvectorB

Returns 1 if at least one corresponding element comparison is false

== and ƒ are on the TEST

menu. round, iPart, fPart, and int are on the MATH NUM menu.

round(vector[,#ofDecimals]) Rounds each vector element to 12 digits, or rounds to specified

#ofDecimals iPart vector

Returns the integer part of each real or complex vector element

fPart vector

Returns the fractional part of each real or complex vector element

int vector

Returns the greatest integer of each real or complex vector element

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13

Matrices TI-86

Matrices on the TI-86 ...................................................... 178 Creating, Storing, and Displaying Matrices...................... 178 Using Mathematical Functions with Matrices.................. 185

M1

M2

M3

M4

M5

F1

F2

F3

F4

F5

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178

Chapter 13: Matrices

Matrices on the TI-86 A matrix is a two-dimensional array, arranged in rows and columns. The matrix elements can be real or complex. You can create, display, and edit matrices on the home screen or in the matrix editor. When you create a matrix, the elements are stored to the matrix name.

Creating, Storing, and Displaying Matrices The MATRX (Matrix) Menu NAMES

EDIT

MATH

-‰ OPS

CPLX

matrix names matrix math complex matrix menu menu menu matrix matrix operations editor menu

The TI-86 distinguishes between uppercase and lowercase letters in matrix names. For example, MAT1 and mat1 are two different vector names.

The MATRX NAMES Menu - ‰ & The MATRX NAMES menu contains all currently stored matrix names in alphanumeric order. To paste a matrix name to the current cursor location, select it from the menu. Creating a Matrix in the Matrix Editor

-‰'



Display the matrix Name= prompt screen.

-‰'



ALPHA-lock is on. The MATRX NAMES menu is displayed. Enter a name from one to eight characters long, starting with a letter.

ãMä ãAä ãTä 11

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Chapter 13: Matrices An ellipsis (…) at either end of matrix rows indicates additional columns.



Display the matrix editor and the matrix editor menu.

b



Accept or change the matrix dimensions (row × column) in the top-right corner of the screen, (1row255 and 1column255); maximum combination is subject to memory availability. The matrix is displayed; all elements are 0.

10 b 4 b



Enter each matrix element value at the element prompt (1,1= for row 1, column 1). You can enter expressions. To move to the next element, press b. To move to the next row, press #.

a4b5 b9b6 b1b a3b7

$ or # in the last column indicates additional rows.

The Matrix Editor Menu INSr

DELr

INSc

b and so on

- ‰ ' matrixName b DELc

4REAL

INSr

Inserts a row at the cursor location; shifts subsequent rows down

DELr

Deletes row at the cursor location; shifts subsequent rows up

INSc

Inserts a column at the cursor location; shifts subsequent columns to the right

DELc

Deletes the column at the cursor location; shifts subsequent columns to the left

4REAL

Converts the displayed complex number matrix to a real number matrix

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179

180

Chapter 13: Matrices

Creating a Matrix on the Home Screen

Define the start of the matrix with ã, and then define the start of the first row with another ã. Enter each element for the row, separating them with commas. Define the end of the first row with ä.

The close bracket is not necessary when it precedes X.



Define the start of each subsequent row with ã . Enter the row elements, separating each from the next with a comma. Define the end of each row with ä. Then define the end of the matrix with ä.

-„a1P a3Pa5P a7- … -…

To delete a matrix name from memory, use the MEM DELETE:MATRX screen (Chapter 17).



Store the matrix to a matrix name. Either enter a name from one to eight characters long, starting with a letter, or select a name from the MATRX NAMES menu. The matrix is displayed. If newly created, the matrix name becomes a MATRX NAMES menu item.

X-n ãMä ãAä ãTä 111 b

-„-„ 2P4P6P 8 -…

Creating a Complex Matrix If any matrix element is complex, all elements of the matrix are displayed as complex. For example, when you enter the matrix [[1,2][5,(3,1)]], the TI-86 displays [[(1,0) (2,0)][(5,0) (3,1)]]. To create a complex matrix from two real matrices with the same dimensions, the syntax is: realMatrix+(0,1)imaginaryMatrix¶complexMatrixName realMatrix contains the real part of each element and imaginaryMatrix contains the imaginary part of each element.

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Chapter 13: Matrices

To view elements beyond the current screen, use ", #, !, and $.

181

Displaying Matrix Elements, Rows, and Submatrices To display an existing matrix on the home screen, enter the matrix name’s individual characters or select it from the MATRX NAMES menu, and then press b. The full value of each element is displayed. Elements with very large values may be expressed exponentially. To display specific elements of matrixName, the syntax is: matrixName(row,column) To display a row of matrixName, the syntax is: matrixName(row) To display a submatrix of matrixName, the syntax is: matrixName(beginRow,beginColumn,endRow,endColumn)

When you execute the expression, the answer is displayed as a matrix.

Using a Matrix in an Expression ♦ You can enter the matrix directly (for example, 5¹[[2,3][3,5]]). ♦ You can use 1 and - n to enter a matrix name’s individual characters (for example, MAT1¹3). ♦ You can select the matrix name from the MATRX NAMES menu (- ‰ &). ♦ You can select the matrix name from the VARS MATRX screen (- w / ').

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Chapter 13: Matrices

Editing Matrices in the Matrix Editor

You can use :, 3, and - p to edit matrix elements. You also can overwrite existing characters.



Display the matrix Name= prompt screen.

-‰'



Enter the matrix name. Either select it from the MATRX NAMES menu or enter the characters.

ãMäãAäãTä 11



Display the matrix editor.

b



Edit or accept the row dimension, and then edit or accept the column dimension.

53b 3b



Move the cursor to any element and edit it. Continue moving the cursor to other elements.

# 45 b " 21 b 2 -



Save the changes and leave the matrix editor.

.

~b

Editing Matrices on the Home Screen To change a matrix element value, the syntax is: value¶matrixName(row,column) To change the values of an entire row of elements, the syntax is: [valueA,valueB,...,value n]¶matrixName(row) To change the values of part of a row, beginning at a specified column, the syntax is: [valueA,valueB,...,value n]¶matrixName(row,beginColumn) To change the values of a submatrix within matrixName, the syntax is: [[valueA,...,value n] ... [valueA,...,value n]]¶matrixName(beginRow,beginColumn)

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Chapter 13: Matrices

The MATRX MATH Menu NAMES det

EDIT T

det squareMatrix

matrix

T

MATH norm

183

-‰( OPS eigVl

CPLX eigVc

4

rnorm

cnorm

LU

cond

Returns the determinant of squareMatrix Returns a transposed matrix; each element’s (row,column) coordinates switch

norm matrix

Returns the Frobenius norm ( G(real 2+imaginary 2)) where the sum is over all elements of a real or complex matrix

eigVl squareMatrix

Returns a list of the normalized eigenvalues of a real or complex squareMatrix

eigVc squareMatrix

Returns a matrix containing the eigenvectors for a real or complex squareMatrix; each column corresponds to an eigenvalue

rnorm matrix

(row norm) Returns the largest of the sums of the absolute values of the elements (magnitudes of complex elements) in each row of matrix

cnorm Matrix

(column norm) Returns the largest of the sums of the absolute values of the elements (magnitudes of complex elements) in each column of matrix

LU(matrix,

Calculates the Crout LU (lower-upper) decomposition of a real or complex matrix; stores the lower triangular matrix to lMatrixName, the upper triangular matrix to uMatrixName, and the permutation matrix (which describes the row swaps done during calculation) in pMatrixName

lMatrixName, uMatrixName, pMatrixName) cond squareMatrix

Calculates cnorm squareMatrix¹cnorm squareMatrixM1 ; the closer the product is to 1, the more stable squareMatrix can be expected to be in matrix functions

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Chapter 13: Matrices

The MATRX OPS (Operations) Menu NAMES dim

Press X to enter the ¶ symbol after the close brace.

EDIT Fill

MATH ident

dim matrix

OPS ref

-‰) CPLX rref

4

aug

4

randM

rSwap

rAdd

multR

mRAdd

Returns the dimensions of matrix as a list {rows columns}

{rows,columns}¶dim matrixName Creates a new matrixName of the specified dimensions; each

element is 0 {rows,columns}¶dim matrixName Redimensions matrixName to the specified dimensions Fill(number,matrixName)

When you use aug(, the number of rows in matrixA must equal the number of rows in matrixB or the number of elements in vector.

Elements of matrices created with randM( are integers ‚L9 and 9.

Stores a real or complex number to each matrixName element

ident dimension

Returns the square identity matrix of dimension × dimension

ref matrix

Returns the row-echelon form of matrix

rref matrix

Returns the reduced row-echelon form of matrix

aug(matrixA,matrixB)

Concatenates matrixA and matrixB

aug(matrix,vector)

Concatenates matrix and vector

rSwap(matrix,rowA,rowB)

Returns a matrix after swapping rowA and rowB of matrix

rAdd(matrix,rowA,rowB)

Returns matrix with (rowA+rowB) of matrix stored in rowB

multR(number,matrix,row)

Returns matrix with (row¹number) stored in row

mRAdd(number,matrix,rowA,rowB) Returns matrix with ((rowA¹number)+rowB) stored in rowB randM(rows,columns)

Creates a matrix of specified dimensions with random elements

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Chapter 13: Matrices

The MATRX CPLX (Complex ) Menu NAMES conj

EDIT real

MATH imag

OPS abs

185

-‰* CPLX angle

conj complexMatrix

Returns a matrix in which each element is the complex conjugate of the corresponding element of a complexMatrix

real complexMatrix

Returns a real matrix in which each element is the real portion of the corresponding element of a complexMatrix

imag complexMatrix

Returns a real matrix in which each element is the imaginary portion of the corresponding element of a complexMatrix

abs matrix

Returns a real matrix in which each element is either the absolute value of the corresponding element of a real matrix or the magnitude (modulus) of the corresponding element of a complex matrix

angle complexMatrix

Returns a real matrix in which each element is either 0 if the element of complexMatrix is real or the polar angle if the element of complexMatrix is complex; the polar angles are calculated as tanL1(imaginary / real) adjusted by +p in the second quadrant and by Lp in the third quadrant

Using Mathematical Functions with Matrices To add or subtract two matrices, the dimensions of matrixA must equal the dimensions of matrixB.

matrixA+matrixB

Adds each matrixA element to the corresponding matrixB element; returns a matrix of the sums

matrixANmatrixB

Subtracts each matrixB element from the corresponding matrixA element; returns a matrix of the differences

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Chapter 13: Matrices

To multiply two matrices, the column dimension of matrixA must equal the row dimension of matrixB.

To enter M1, press - ƒ. Do not use 2 @ a 1.

e^, sin, and cos do not return

the exponential, sine, or cosine of each matrix element. To make relational comparisons, matrixA and matrixB must have equal dimensions.

matrixA¹matrixB or matrixB¹matrixA

Multiplies matrixA and matrixB; returns a square matrix of the products

matrix¹number or number¹matrix

Returns a matrix that is the product of a real or complex number times each element in a real or complex matrix

matrix¹vector

Returns a vector that is the product of each vector element times each matrix element; the matrix column dimension and vector dimension must be equal

Mmatrix

(negation) Changes the sign of each element in matrix

squareMatrix M 1

Returns the inverse of squareMatrix (not the inverse of each element)

matrix 2

Squares a square matrix

squareMatrix^power

Raises a squareMatrix to the designated power

e^ squareMatrix

Returns the square matrix exponential of a real squareMatrix

sin squareMatrix

Returns the square matrix sine of a real squareMatrix

cos squareMatrix

Returns the square matrix cosine of a real squareMatrix

matrixA==matrixB

Returns 1 if every corresponding element comparison is true; returns 0 if any is false

matrixAƒmatrixB

Returns 1 if at least one corresponding element comparison is false

round(matrix[,#ofDecimals]) Rounds each matrix element to 12 digits or to specified #of Decimals == and ƒ are on the TEST

menu. round, iPart, fPart, and int are on the MATH NUM menu.

iPart matrix

Returns the integer part of each element of a real or complex matrix

fPart matrix

Returns the fractional part of each element of a real or complex matrix

int matrix

Returns the greatest integer of each element of a real or complex matrix

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14

Statistics TI-86

Statistical Analysis on the TI-86 ...................................... 188 Setting Up a Statistical Analysis....................................... 188 Results of a Statistical Analysis........................................ 192 Plotting Statistical Data ................................................... 194 The STAT DRAW Menu .................................................... 199 Forecasting a Statistical Data Value ................................ 199

M1

M2

M3

M4

M5

F1

F2

F3

F4

F5

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Chapter 14: Statistics

Statistical Analysis on the TI-86 With the TI-86, you can analyze one-variable and two-variable statistical data, which are stored in lists. One-variable data has one measured variable. Two-variable data has pairs comprising an independent variable and a dependent variable. When analyzing either kind of data, you can specify a frequency of occurrence for the independent variable values. These specified frequencies must be real numbers ‚ 0.

Setting Up a Statistical Analysis

Enter the statistical data into one or more lists (Chapter 11).



Calculate the statistical variables or fit a model to the data.



Plot the data.



Graph the regression equation for the plotted data.

The STAT (Statistics) Menu The same list editor is displayed, whether you press - š ' or - ” ). For a description of the list editor, see Chapter 11.

CALC

EDIT

PLOT

-š DRAW

VARS

4

statistical stat plot statistical result calculations menu variables menu menu list editor statistical drawing tools menu

FCST

forecast editor

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Chapter 14: Statistics

189

Entering Statistical Data Data for statistical analysis is stored in lists, which you can create and edit in the list editor (Chapter 11), on the home screen (Chapter 11), or in a program (Chapter 16). The TI-86 has three built-in list names for statistics, xStat (x-variable list), yStat (y-variable list), and fStat (frequency list). TI-86 statistical functions use these lists as defaults. The LIST NAMES Menu The LIST NAMES menu shown here has no usercreated list names. Editing an element of xStat or yStat clears any values stored to statistical result variables.

{ fStat

} xStat

NAMES yStat

-š'( EDIT

fStat

An automatically updated list of the frequency values used in the last statistical computation requiring a frequency; default is a list where each element is 1

xStat

An automatically updated list of the data from the x-list used in the last statistical analysis

yStat

An automatically updated list of the data from the y-list used in the last statistical analysis

The STAT CALC (Calculations) Menu The STAT CALC functions store the results to statistical result variables (page 193 ).

The syntax description for each STAT CALC menu item follows this section.

OPS

CALC OneVa

OneVa TwoVa

EDIT TwoVa

PLOT LinR

DRAW LnR

-š& VARS ExpR

4

PwrR

SinR

4

P4Reg

StReg

(one variable) Analyzes data with one measured variable (two variable) Analyzes paired data

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LgstR

P2Reg

P3Reg

190

Chapter 14: Statistics

For regression analysis, the statistical results are calculated using a leastsquares fit.

SinR and LgstR are

LinR LnR

(linear regression) Fits the model equation y=a+bx to the data; displays values for a (slope) and b (y-intercept) (logarithmic regression) Fits the model equation y=a+b ln x to the data using transformed values ln(x) and y; displays values for a and b

ExpR

(exponential regression) Fits the model equation y=abx to the data using transformed values x and ln(y); displays values for a and b; elements in the x-list and y-list elements must be integers

PwrR

(power regression) Fits the model equation y=axb to the data using transformed values ln(x) and ln(y); displays values for a and b

SinR

(sinusoidal regression) Fits the model equation y=a¹sin(bx+c)+d to the data; displays values for a, b, c, and d; SinR requires at least four data points; it also requires at least two data points per cycle to avoid aliased frequency estimates

LgstR

(logistic regression) Fits the model equation y=aà(1+becx)+d to the data; displays a, b, c, and

calculated using an iterative least-squares fit.

d P2Reg

(quadratic regression) Fits the second-degree polynomial y=ax2+bx+c to the data; displays values for a, b, and c; for three data points, the equation is a polynomial fit; for four or more, it is a polynomial regression; P2Reg requires at least three data points

P3Reg

(cubic regression) Fits the third-degree polynomial y=ax3+bx2+cx+d to the data; displays values for a, b, c, and d; for four points, the equation is a polynomial fit; for five or more, it is a polynomial regression; P3Reg requires at least four data points

P4Reg

(quartic regression) Fits the fourth-degree polynomial y=ax4+bx3+cx2+dx+e to the data; displays values for a, b, c, d, and e; for five points, the equation is a polynomial fit; for six or more, it is a polynomial regression; P4Reg requires at least five data points

StReg

(store regression equation) Pastes StReg( to the home screen; enter a variable and press b; the current regression equation is stored to variable

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Chapter 14: Statistics When you select OneVa or TwoVa, the abbreviation OneVar or TwoVar is displayed.

For OneVa, the syntax is:

For PwrR and ExpR, the elements of xList and yList must be integers ‚ 1.

For LinR, LnR, ExpR, PwrR, P2Reg, P3Reg, and P4Reg, the syntax is:

191

OneVar ãxList,frequencyListä

For TwoVa, the syntax is: TwoVar ãxLlist,yList,frequencyList ä TwoVar ãxList,yList,frequencyListä

For SinR, the syntax is: SinR ãiterations,xList,yList,period,equationVariableä Default for iterations is 64.

iterations is the number of iterations to go through; higher values for iterations produce a better fit, but take longer to calculate. period is an initial guess at which to begin calculation. For LgstR, the syntax is: LgstR ãiterations,xList,yList,frequencyList,equationVariableä

To copy the contents RegEq to any variable after calculating the regression, the syntax is: StReg(variable)

Automatic Regression Equation Storage LinR, LnR, ExpR, PwrR, SinR, LgstR, P2Reg, P3Reg, and P4Reg are regression models. Each regression model has an optional argument, equationVariable, for which you can specify an equation variable, such as y1. Upon execution, the regression equation is stored automatically to the specified equation variable, and the function is selected. Regardless of whether you specify equationVariable, the regression equation always is stored to the result variable RegEq, which is an item on the STAT VARS menu. The regression equation displays the actual result values.

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Chapter 14: Statistics

PRegC is the only statistical

result variable calculated for a polynomial regression.

The result for a polynomial regression, sinusoidal regression, or logistic regression is stored in PRegC (polynomialàregression coefficients). PRegC is a list containing the coefficients for an equation. For example, for P3Reg, the result PRegC={3 5 L2 7} would represent y=3x3+5x2N2x+7.

Results of a Statistical Analysis One- and two-variable statistical functions share the result variables.

When you perform a statistical analysis, the calculated results are stored in the result variables and the data from the lists used in the analysis are stored to xStat, yStat, and fStat. If you edit a list or change the type of analysis, all statistical variables are cleared. CALC v

The statistical variables are calculated and stored as shown in the table on the next page.

You can use ALPHA keys, alpha keys, and the CHAR GREEK menu to enter some result variables.

-š*

The STAT VARS (Statistical Variables) Menu EDIT sx

PLOT Sx

DRAW w

VARS sy

4

Sy

Gx

Gx2

Gy

Gy2

4

Gxy

RegEq

corr

a

b

4

n

minX

maxX

minY

maxY

4

Med

PRegC

Qrtl1

Qrtl3

tolMe

To paste a result variable to the cursor location, either select the variable from the STAT VARS menu or select the variable from the VARS STAT selection screen.

♦ ♦ ♦

To use a result variable in an expression, paste it to the appropriate cursor location. To display the value of a result variable, paste it to the home screen and press b. To store results to another variable after a calculation, paste the result variable to the home screen, press X, enter a new variable, and then press b.

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Chapter 14: Statistics

These words are abbreviated in the table: pop = population std dev = standard deviation coeff = coefficient int = intercept reg eq = regression equation pts = points min = minimum max = maximum

Result Variables

1-Var Stats

2-Var Stats

mean of x values

v

v

correlation coeff

corr

sx

sx

y-intercept of reg eq

a

sample std dev of x Sx mean of y values

Sx

slope of reg eq

b

w

regressionàfit coeff

a, b

pop std dev of y

sy

number of data pts

n

n

sample std dev of y

Sy

min of x values

minX

minX

maxX

maxX

pop std dev of x

Other

Result Variables

1-Var Stats

2-Var Stats

Other

sum of x values

Gx

Gx

max of x values

sum of x2 values

Gx2

Gx2

min of y values

minY

Gy

max of y values

maxY

Gy2

median

Gxy

1st quartile

Qrtl1

sum of y values 2

sum of y values sum of x ¹ y

Med

regression equation

RegEq

3rd quartile

Qrtl3

polynomial, LgstR, and SinR coeff’s

a (y-int) b (slope)

polynomial LgstR, and SinR reg coeff’s

PRegC

The first quartile (Qrtl1) is the median of the points between minX and Med (median). The third quartile (Qrtl3) is the median of the points between Med and maxX. When you calculate a logistic regression, 1 is stored to tolMet (tolMe) if the TI-86 internal tolerance was met before the calculator arrived at a result; if not met, 0 is stored to tolMet.

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Chapter 14: Statistics

Plotting Statistical Data You can plot one, two, or three sets of statistical list data. The five available plot types are scatter plot, xyLine, histogram, modified box plot, and regular box plot.

Store the statistical data in one or more lists (Chapter 11).



Select or deselect functions in the current equation editor as appropriate (Chapter 5).



Define the statistical plot.



Turn on the plots you want to display.



Define the window variables for the graph screen (Chapter 5).



Display and explore the plotted graph (Chapter 6).

The STAT PLOT Status Screen - š ( The STAT PLOT status screen summarizes the settings for Plot1, Plot2, and Plot3. The illustration below identifies the settings for Plot1. This screen is not interactive. To change a setting, select PLOT1, PLOT2, or PLOT3 from the STAT PLOT status screen menu. This screen shows the default stat plot settings. If you select another plot type, some prompts may change.

Stat plot name

OnàOff status

1:Plot1...Off

Plot-type icon

® xStat

Independent list name

yStat



Mark-type icon

Dependent list name

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Chapter 14: Statistics

When you display a stat plot editor, the STAT PLOT menu remains so that you can easily switch to another stat plot.

In this guidebook, brackets ( ã and ä ) with syntax specify arguments as optional. Do not enter brackets, except with vectors and matrices.

You need not turn on a stat plot to change the settings.

You also can use STAT PLOT menu items PlOn or PlOff to turn on or turn off stat plots.

195

The STAT PLOT Menu - š ( PLOT1 PLOT2 PLOT3 PlOn PlOff PLOT1

Displays the stat plot editor for Plot1

PLOT2

Displays the stat plot editor for Plot2

PLOT3

Displays the stat plot editor for Plot3

PlOn [1,2,3]

Turns on all plots (if you enter no arguments) or turns on specified plots only

PlOff [1,2,3]

Turns off all plots (if you enter no arguments) or turns off specified plots only

To turn on or turn off all three stat plots, select PlOn or PlOff from the STAT PLOT menu. PlOn or PlOff is pasted to the home screen. Press b. All stat plots are now on or off. Setting Up a Stat Plot To set up a stat plot, select PLOT1, PLOT2, or PLOT3 from the STAT PLOT menu. The stat plot editor for the selected stat plot is displayed. Each stat plot type has a unique stat plot editor. The screen to the right shows the stat plot editor for the default ® (scatter plot). If you select another plot type, some prompts may change. Turning On and Turning Off a Stat Plot When you display a stat plot editor, the cursor is on the On option. ♦ To turn on the stat plot, press b. ♦ To turn off the stat plot, press " b.

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Chapter 14: Statistics

The PLOT TYPE Menu (Selecting a Plot Type) To display the PLOT TYPE menu, move the cursor onto the plot type icon at the Type= prompt. When you select a plot type, the appearance of the stat plot editor may change.

PLOT1 PLOT2 PLOT3 SCAT xyLINE MBOX

In these stat plot examples, all functions are deselected. Also, menus are cleared from the screen with :.

PlOff BOX

At this prompt...

Enter this information:

Default is:

Displayed menu is:

Xlist Name=

independent-data list name

xStat

LIST NAMES menu

Ylist Name=

dependent-data list name

yStat

LIST NAMES menu

Freq=

frequency list name (or 1)

fStat (default value: 1)

LIST NAMES menu

Mark=

plot mark (› or + or ¦)



♦ ♦ ♦

Stat plots are displayed on the graph screen (6 *), as defined by the window variable values (Chapter 5). Some graph tools apply to stat plots.

PlOn HIST

(none for HIST or BOX)

PLOT MARK menu

Any list you enter at the Xlist Name= prompt is stored to the list name xStat. Any list you enter at the Ylist Name= prompt is stored to the list name yStat. Any list you enter at the Freq= prompt is stored to fStat.

Plot Type Characteristics ® SCAT (scatter plot) plots the data points from Xlist Name and Ylist Name as coordinate pairs, representing each point with a box ( › ), cross ( + ), or dot ( ¦ ) mark type. Xlist Name and Ylist Name must be the same length. Xlist Name and Ylist Name can be the same list. For the example: xStat={1 2 3 4 5 6 7 8 9 10} yStat=5 sin(xStat)

Window variable values: xMin=0 xMax=10

yMin=L10 yMax=10

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− xyLINE is a scatter plot in which the data points are plotted and connected in order of appearance in Xlist Name and Ylist Name. You may want to use SortA or SortD from the LIST OPS menu (Chapter 11) to sort the lists before you plot them. For the example: xStat={1 2 3 4 5 6 7 8 9 10} yStat=5 sin(xStat)

Window variable values: xMin=0 xMax=10

yMin=L10 yMax=10

¯ MBOX (modified box plot) plots one-variable data, like the regular box plot, except that the points are 1.5 ¹ Interquartile Range beyond the quartiles. (The Interquartile Range is defined as the difference between the third quartile Q3 and the first quartile Q1.) These points are plotted individually beyond the whisker, using the Mark ( › or + or ¦ ) you select. For the example: xStat={1 2 2 2.5 3 3.3 4 4 2 6 9}

Window variable values are set by selecting ZDATA from the GRAPH ZOOM menu.

Whiskers are the lines protruding from the sides of the box.

You can trace these points, which are called outliers. When outliers exist, the end of each whisker will display an x= prompt. When no outliers exist, xMin and xMax are the prompts for the end of each whisker. Q1, Med (median), and Q3 define the box. Modified box plots are plotted with respect to xMin and xMax, but ignore yMin and yMax. When two modified box plots are plotted, the first one plots at the top of the screen and the

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Chapter 14: Statistics

second plots in the middle. When three are plotted, the first one plots at the top, the second in the middle, and the third at the bottom. ¬ HIST (histogram) plots one-variable data. The xScl window variable value determines the width of each bar, beginning at xMin. ZDATA (GRAPH ZOOM menu) adjusts xMin, xMax, yMin, and yMax to include all values, and also adjusts xScl. (xMax N xMin) à xScl  47 must be true. A value that occurs on the edge of a bar is counted in the bar to the right. For the example: xStat={1 2 2 2 3 8 9 5 6 6 7 7 4 4 9 9 9}

Window variable values: xMin=0 xMax=10

Whiskers are the lines protruding from the sides of the box.

yMin=0 yMax=5

° BOX (regular box plot) plots one-variable data. The whiskers on the plot extend from the minimum data point in the set (xMin) to the first quartile (Q1) and from the third quartile (Q3) to the maximum point (xMax). The box is defined by Q1, Med (median), and Q3. For the example: xStat={1 2 2 2.5 3 3.3 4 4 2 6 9}

Window variable values are set by selecting ZDATA from the GRAPH ZOOM menu.

Box plots are plotted with respect to xMin and xMax, but ignore yMin and yMax. When two box plots are plotted, the first one plots at the top of the screen and the second plots in the

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Chapter 14: Statistics

199

middle. When three are plotted, the first one plots at the top, the second in the middle, and the third at the bottom.

The STAT DRAW Menu CALC HIST When you select any of the first five STAT DRAW menu items, the TI-86 plots the data stored in the lists xStat and yStat.

EDIT SCAT

PLOT DRAW xyLINE BOX

-š) VARS MBOX

4

DRREG CLDRW DrawF

STPIC

HIST

Draws a histogram of one-variable data

SCAT

Draws a scatter plot of the data points

xyLINE

Draws the data points and a line connecting each point to the next point

BOX

Draws a box plot of the data points

MBOX DRREG

Draws a modified box plot of the data points (draw regression equation) Draws the current regression equation

CLDRW

(clear drawings) Displays the current graph with no drawings

RCPIC

DrawF expression (draw function) Plots expression as a drawing STPIC

(store picture) Displays the picture variable Name= prompt; enter a valid variable name, starting with a letter, and then press b to store the current picture

RCPIC

(recall picture) Displays the picture variable Name= prompt and menu; select or enter a valid variable name, and then press b; the stored picture is redrawn

Forecasting a Statistical Data Value Using the forecast editor, you can forecast an x-value or y-value based on the current regression equation. To use the forecast editor, a regression equation must be stored to RegEq.

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Chapter 14: Statistics

Enter stat data in the list editor. The screen to the right shows all fStat elements as 1, but you need not enter them. 1 is the default for all fStat elements. However, if other elements are stored to fStat, you must clear them.

-š'



Display the home screen.

.



Execute a linear regression for xStat and yStat. The statistical results are displayed.

-š& (b



Remove the STAT CALC menu to display all results, including n.

.



Display the forecast editor. The current regression model is displayed on the top line.

/&

Values entered at forecast editor prompts must be real numbers or expressions that evaluate to real numbers.



Enter x=3 , and then move the cursor to the y= prompt.



Select SOLVE from the forecast editor menu to solve for y at x=3. A small square indicates the solution. You can continue to use the forecast editor with other values for x or y.

If the most recent calculation was a polynomial regression, you can only forecast the y value.

When you use FCST, the values of x, y, and Ans are not updated. To store the x value or y value, move the cursor onto the variable to be stored, press X, enter a valid variable name at the Sto prompt, and then press b.

`1#1`1 #2#4#5 #"1#2 #3#4#2

3#

*

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15

Equation Solving TI-86

Preview: The Equation Solver .......................................... 202 Entering an Equation in the Equation-Entry Editor .......... 203 Setting Up the Interactive-Solver Editor........................... 204 Solving for the Unknown Variable ................................... 206 Graphing the Solution...................................................... 207 Solver Graph Tools........................................................... 207 The Simultaneous Equation Solver .................................. 208 The Polynomial Root-Finder............................................. 211 M1

M2

M3

M4

M5

F1

F2

F3

F4

F5

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Chapter 15: Equation Solving

Preview: The Equation Solver

-t

With the equation solver, you can enter an expression or equation, store values to all but one variable in the expression or equation, and then solve for the unknown variable. These steps introduce the solver. For details, read this chapter. The VARS EQU menu is a menu version of the VARS EQU screen (Chapter 2).



Display the equation-entry editor. The VARS EQU menu is displayed on the bottom of the screen.

The example uses a formula for a voltage divider.



Enter an equation. When you press b, the interactive-solver editor and solver menu are displayed.



Enter values for each variable, except the unknown variable R1. Some variables may have values stored to them already.

10 # 100 # # 57



Move the cursor to the variable for which you want to solve. You may enter a guess.

$



Solve the equation for the variable. Small squares mark both the solution variable and the equation leftNrt=0 (the left side of the equation minus the right side of the equation). If you edit a value or leave the screen, the squares disappear.

*

R1 and R2 represent resistors. V and V1 represent voltage.

To solve for the unknown variable in an equation on the home screen or in the program editor, select Solver( from the CATALOG (A to Z Reference).

-t 1 ãVä 1 1 ã=ä 1 ãVä D 1 ã Rä 1 F D 1 ãRä 1 \ 1 ãRä 2 E E b

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Entering an Equation in the Equation-Entry Editor The equation solver uses two editors: the equation-entry editor, where you enter and edit the equation you want to solve, and the interactive-solver editor, where you enter known variable values, select the variable for which you want to solve, and display the solution.

The equation can have more than one variable to the left of the equal sign, as in A+B=C+sin D.

To display the equation-entry editor, press - t. In this editor, you can: ♦ Enter an equation directly. ♦ Enter a defined equation variable’s individual characters or select it from the VARS EQU menu. ♦ Recall the contents of a defined equation variable. As you enter or edit the equation, the TI-86 automatically stores it to the variable eqn.

You can display other menus in the equation-entry editor. An ellipsis (...) indicates that an entered equation continues beyond the screen. To move directly to the start of the equation, press - !; to move directly to the end, press - ".

The VARS EQU menu is a menu version of the VARS EQU screen (Chapter 2). The items are all variables to which an equation is stored. This includes all selected and deselected equation variables defined in the equation editors of all four graphing modes (Chapters 5, 8, 9, and 10). The menu items are in alphanumeric order. ♦ If you select an equation variable from the menu, the variable is pasted to the cursor location, overwriting characters for the length of the variable name. ♦ If you press - –, select an equation variable from the menu, and then press b, the variable contents are inserted at the cursor location. If you enter an equation variable, the TI-86 automatically converts it to the equation exp=equationVariable. If you enter an expression directly, the TI-86 automatically converts the expression to the equation exp=expression.

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Chapter 15: Equation Solving

Setting Up the Interactive-Solver Editor In the example, the equation V1=V(R1à(R1+R2)) was entered in the equation-entry editor. If you entered an expression for eqn, then exp= is the first variable prompt on the interactive-solver editor.

After you have stored an equation to eqn in the equation-entry editor, press b to display the interactive-solver editor. The equation is displayed across the top of the editor. Each variable in the equation is displayed as a prompt. Values already stored to variables are displayed; undefined variables are blank. The solver menu is displayed on the bottom of the editor (page 206). bound={L1E99,1E99} is a list containing the default lower bound (L1E99) and the default upper bound (1E99). You can edit the bounds (below).

Entering Variable Values To solve for an unknown variable, you must define every other variable in the equation. When you enter or edit a variable value in the interactive-solver editor, the new value is stored to the variable in memory. For any variable, you may enter an expression, which is evaluated when you press b, #, $, or .. Expressions must resolve to real numbers at each step of the calculation. Controlling the Solution with Bounds and a Guess The solver seeks a solution only within the specified bounds. Whenever you display the interactive-solver editor, the default bound={L1E99,1E99} is displayed. These are the maximum bounds for the TI-86.

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Chapter 15: Equation Solving

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The TI-86 solves equations through an iterative process. To control that process, you can enter lower bounds and upper bounds that are close to the solution, and enter a guess within those bounds in the prompt for the unknown variable. Controlling the process with specific bounds and a guess helps the TI-86 in two ways. ♦ It finds a solution more quickly. ♦ It is more likely to find the solution you want when an equation has multiple solutions. lowerBound
To set more precise bounds at the bound= prompt, the syntax is: bound={lowerBound,upperBound}

You can enter a list variable at the bound= prompt if a valid two-element list is stored to it.

At the prompt for the unknown variable, you may enter a guess or a list of two guesses. If you do not enter a guess, the TI-86 uses (lowerBound+upperBound)à2 as a guess.

If you exit the equation solver, any equation stored to eqn is displayed when you return to the equation solver.

On the solver graph (page 207), you can guess a solution by moving the free-moving cursor or trace cursor to a point on the graph between lowerBound and upperBound. To solve for the unknown variable using the new guess, select SOLVE from the solver graph menu. The solution is displayed on the interactive-solver editor. Editing the Equation To edit the equation stored to eqn when the interactive-solver editor is displayed, press $ until the cursor is on the equation. The equation-entry editor is displayed. The TI-86 automatically stores the edited equation to eqn as you edit. If you store an equation to eqn by recalling the contents of an equation variable, such as y1, and then edit the equation stored to eqn, the original equation (in y1, for example) is not changed. Likewise, subsequently editing the contents of the equation variable (y1, for example) does not change eqn.

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Chapter 15: Equation Solving

The Solver Menu You can display other menus in the interactive-solver editor

GRAPH

WIND

- t equation b ZOOM

TRACE SOLVE

graphs the solver zoom solves for the unknown variable or menu displays the interactive-solver editor equation in eqn window graphs eqn and editor activates the trace cursor

To display the window editor, select WIND from the solver menu. When you select GRAPH or WIND from the solver menu, EDIT replaces the item you selected on the menu. To return to the interactive-solver editor from the graph or window editor, select EDIT.

Solving for the Unknown Variable After you have stored all known variable values, set the bounds, and entered a guess (optional), move the cursor to the prompt for the unknown variable. An ellipsis (...) indicates that the variable value continues beyond the screen. To scroll the value, press " and !. The squares disappear when you edit any value. After solving, you can edit a variable value or edit the equation, and then solve for the same variable or another variable in the equation.

To solve, select SOLVE from the solver menu (*). ♦ A small square marks the variable for which you solved. The solution value is displayed. ♦ A small square also marks the leftNrt= prompt. The value at this prompt is the value of the left side of the equation minus the value of the right side of the equation, evaluated at the new value of the variable for which you solved. If the solution is precise, leftNrt=0 is displayed. Some equations have more than one solution. To look for additional solutions, you can enter a new guess or set new bounds, and then solve for the same variable.

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Graphing the Solution The graph to the right plots the solution from the example on page 202. The window variable values are: xMin=L10 yMin=L50 xMax=50

yMax=50

When you select GRAPH from the solver menu (&), the solver graph is displayed with the free-moving cursor. ♦ The vertical axis represents the result of the left side of the equation minus the right side of the equation (leftNright) at each independent variable value. ♦ The horizontal axis represents the independent variable for which you solved the equation. On the graph, solutions exist for the equation where leftNrt=0, which is where the graph intersects the x-axis. The solver graph: ♦ ♦ ♦ ♦

Uses the current window and format settings (Chapter 5). Does not graph the solution according to the current graphing mode. Always graphs a solution as a function graph. Does not graph selected functions or turned on stat plots along with the solution.

Solver Graph Tools You can use the free-moving cursor or trace cursor to select a guess on the graph.

You can explore the graph of a solution with the free-moving cursor, as you would on any other graph. When you do, the coordinate values for the variable (the x-axis) and the value leftNrt (the y-axis) are updated. To activate the trace cursor, select TRACE from the solver menu. Panning, QuickZoom, and entering a specific value (Chapter 6) are available with the trace cursor on the solver graph. To return to the solver menu from a trace, press ..

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Chapter 15: Equation Solving

The Solver ZOOM Menu GRAPH BOX Chapter 6 and the A to Z Reference describe these features in detail.

WIND ZIN

ZOOM ZOUT

- t equation b ( TRACE SOLVE ZFACT ZSTD

BOX

Draws a box to redefine the viewing window (Chapter 6)

ZIN

Magnifies the graph around the cursor by factors of xFact and yFact (Chapter 6)

ZOUT

Displays more of the graph around the cursor by factors of xFact and yFact (Chapter 6)

ZFACT

Displays the ZOOM FACTORS screen (Chapter 6)

ZSTD

Displays the graph in standard dimensions; resets the default window variable values for Func graphing mode

The Simultaneous Equation Solver

-u

The simultaneous equation solver solves systems of up to 30 linear equations with 30 unknowns. Entering Equations to Solve Simultaneously The SIMULT coefficients are not variables. You can display other menus in the coefficients-entry screen.



Display the SIMULT number screen.

-u



Enter an integer ‚ 2 and  30 for the number of equations. The coefficientsentry editor for the first equation (for a system of n equations and n unknowns) is displayed. The SIMULT ENTRY menu also is displayed.

3b

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Chapter 15: Equation Solving To move from the coefficients-entry editor for one equation to the editor for another equation, select PREV or NEXT.



Enter a real or complex value (or an expression that resolves to one) for each coefficient in the equation and for b 1 , which is the solution to that equation.

9#8#7#2

To move among coefficients, press #, $, or b. From the last or first coefficient, these keys move to the next or previous coefficients-entry screen, if possible.



Display the coefficients-entry screen for the second and third equation, and enter values for them.

# (or b or ') 5 # a 6 # a 4#2 #1#5#9#7



Solve the equations. The results of the polynomial are calculated and displayed on the result screen. Results are not stored to variables and cannot be edited. The SIMULT RESULT menu is displayed.

*

Ellipses indicate that a value continues beyond the screen. Press " and ! to scroll the value.

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210

Chapter 15: Equation Solving

Storing Equation Coefficients and Results to Variables ♦ To store coefficients a 1,1; a 1,2;...;a n,n to an n×n matrix, select STOa. ♦ To store solutions b 1,b 2,...,bn to a vector of dimension n, select STOb. ♦ To store the results x 1, x 2,..., x n to a vector of dimension n, select STOx. To store a single value on the coefficients-entry screen or result screen, follow these steps. To switch to the coefficientsentry screen, select COEFS from the SIMULT RESULT menu.

To solve equations simultaneously on the home screen or in a program, select simult( from the CATALOG.



Move the cursor to the = sign next to the coefficient or result you want to store.

#



Display the variable Name= prompt. ALPHA-lock is on.

X



Enter the variable to which you want to store the value.

ãRä ãEä ãSä ãUä ãLä ãTä 1 2



Store the value. The variable name becomes an item on the VARS REAL screen or VARS CPLX screen.

b

To return to the coefficients-entry screen, where you can edit coefficients and calculate new solutions, select COEFS from the SIMULT RESULT menu.

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Chapter 15: Equation Solving

The Polynomial Root-Finder

-v

The root finder solves up to 30th-order real or complex polynomials. Entering and Solving a Polynomial The POLY coefficients are not variables. You can display other menus in the coefficients-entry editor.



Display the POLY order screen.

-v



Enter an integer between 2 and 30. The coefficients-entry editor is displayed with the equation across the top, the coefficient prompts along the left side, and the POLY ENTRY menu on the bottom.

4b



Enter a real or complex value (or an expression that resolves to one) for each coefficient.

18 # 5 # 21 # 7 # 16

To clear all coefficients, select CLRa from the POLY ENTRY menu. Ellipses indicate that a value continues beyond the screen. Press " and ! to scroll the value.



Solve the equation. The roots of the polynomial are calculated and displayed. Results are not stored to variables and you cannot edit them. Also, the POLY RESULT menu is displayed. Results can be complex numbers.

*

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212

Chapter 15: Equation Solving

Storing a Polynomial Coefficient or Root to a Variable To switch to the coefficientsentry screen, select COEFS from the POLY RESULT menu.

To find roots on the home screen or in a program, select poly from the CATALOG.



Move the cursor to the = sign next to the coefficient or root value you want to store.

###



Display the Sto prompt. ALPHA-lock is on.

X



Enter the variable to which you want to store the value.

ãRä ãOä ãOä ãTä 11



Store the value.

b



Display the Name= prompt for the coefficents list name. ALPHA-lock is on.

'



Enter the list variable name to which you want to store the coefficients.

ãCä ãOä ãEä ãFä 11



Store the polynomial coefficient values.

b

To return to the coefficients-entry screen, where you can edit coefficients and calculate new solutions, select COEFS from the POLY RESULT menu.

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16

Programming TI-86

Writing a Program on the TI-86 ....................................... 214 Running a Program.......................................................... 221 Working with Programs ................................................... 223 Running an Assembly Language Program ....................... 225 Entering and Storing a String........................................... 226

M1

M2

M3

M4

M5

F1

F2

F3

F4

F5

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Chapter 16: Programming

Writing a Program on the TI-86 A program is a set of expressions, instructions, or both, which you enter or download. Expressions and instructions in the program are executed when you run the program. You can use most TI-86 features in a program. Programs can retrieve and update all variables stored to memory. Also, the program editor menu has inputàoutput commands, such as Input and Disp, and program control commands, such as If, Then, For, and While. The PRGM Menu NAMES

8

EDIT

program program editor names menu

The TI-86 distinguishes between uppercase and lowercase letters in program names. For example, ABC, Abc, and abc would be three different program names.

Creating a Program in the Program Editor To begin writing a program, select EDIT from the PRGM menu (8 '). The program Name= prompt and PRGM NAMES menu are displayed. ALPHA-lock is on. Enter a program name from one to eight characters long, beginning with a letter. To edit an existing program, you can select the name from the PRGM NAMES menu.

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215

After you enter a program name, press b. The program editor and program editor menu are displayed. The program name is displayed at the top of the screen. The cursor is on the first command line, which begins with a colon. The TI-86 automatically places a colon at the beginning of each command line. As you write the program, the commands are stored to the program name. The Program Editor Menu PAGE$ PAGE# page down

IàO

8 ' programName b CTL

INSc

DELc

UNDEL

:

inputàoutput menu

insert a blank undelete (paste) a command line deleted command line program delete (cut) a paste a control menu command line colon

page up

The PRGM IàO (InputàOutput) Menu PAGE$ PAGE# Input Promp The PRGM IàO menu items are instructions. The actions they perform occur as the program runs.

4

IàO Disp

CTL DispG

8 ' programName b (

INSc DispT

4

ClTbl

Get

Send

4

"

Outpt

InpSt

getKy

ClLCD

To see examples that show how to use PRGM IàO menu items in programs, refer to the A to Z Reference.

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Chapter 16: Programming

Input

Displays the current graph and lets you use the free-moving cursor

Input variable

Pauses a program, displays ? as a prompt, and then stores your response to variable

If you enter an expression for variable at an Input or Prompt prompt, it is evaluated and stored.

Input promptString,variable Input "string",variable

Pauses a program, displays promptString or string (up to 21 characters) as a prompt, and then stores your response to variable

Input "CBLGET",variable

Although using Get( is preferred on the TI-86, you can use Input to receive variable from a CBL 2/CBL, CBR, or TI-86 (TI-85 compatible)

For Input and Prompt, built-in variables such as y1 and r1 are not valid as variable.

Prompt variableA ã,variableB,variableC,...ä

Displays each variable with ? to prompt you to enter a value for that variable

To halt the program temporarily after Disp or DispG and examine what the program is displaying, enter Pause on the next command line (page 219).

Disp

Displays the home screen

Disp valueA,valueB,...

Displays each value

Disp variableA,variableB,...

Displays the value stored to each variable

Disp "textA","textB",...

Displays each text string on the left side of the current display line

DispG

Displays the current graph

DispT

Displays the current table and temporarily halts the program

ClTbl

Clears the current table if Indpnt: Ask is set (Chapter 7)

Get(variable)

Gets data from a CBL 2/CBL, CBR, or another TI-86 and stores it to variable

Send(listName)

Sends the contents of listName to a CBL 2/CBL or CBR

getKy

Returns a number corresponding to the last key pressed, according to the key code diagram (page 217); if no key was pressed, returns 0

ClLCD

Clears the home screen (LCD stands for liquid crystal display)

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"string"

Specifies the beginning and end of a string

Outpt(row,column,"string") Outpt(row,column,stringName) Outpt(row,column,value) Outpt(row,column,variable)

Displays string, stringName, value, or a value stored to variable beginning at the specified row and column on the display

Outpt("CBLSEND",listName)

Although using Send( is preferred on the TI-86, you can use Outpt( to send listName to a CBL 2/CBL or CBR (for TI-85 compatibility)

InpSt promptString,variable InpSt variable

Pauses a program, displays promptString or ?, and waits for a response; stores the response to variable always as a string; omit quotation marks from your response

The TI-86 Key Code Diagram When getKy is encountered in a program, it returns a number corresponding to the last key pressed, according to the key code diagram to the right. If no key has been pressed, getKy returns 0. Use getKy inside loops to transfer control, such as when you create a video game. This program returns the key code of each key you press. :Float :0¶A :Lbl TOP :getKy¶A :If A>0 :Disp A :Goto TOP

To break (interrupt) the program, press ^ and then press *.

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Chapter 16: Programming

The PRGM CTL Menu PAGE$ PAGE# If Then

8 ' programName b )

IàO Else

CTL For

INSc End

4

While

Repea

Menu

Lbl

Goto

4

IS>

DS<

Pause

Retur

Stop

4

DelVa

GrStl

LCust

To see examples that show how to use PRGM CTL menu items in programs, refer to the A to Z Reference. If, While, and Repeat

instructions can be nested.

For( loops can be nested.

If condition

If condition is false (evaluates to 0), the next program command is skipped; if condition is true (evaluates to a nonzero value), the program continues on to the next command

Then

Following If, executes a group of commands if condition is true

Else

Following If and Then, executes a group of commands if condition is false

For(variable,begin,end ã,stepä)

Starting at begin, repeats a group of commands by an optional real step until variable > end; default step is 1

End

Identifies the end of a group of program commands; For(, While, Repeat, and Else groups must end with End; Then groups without an associated Else instruction also must end with End

While condition

Repeats a group of commands while condition is true; condition is tested when the While instruction is encountered; typically, the expression that defines condition is a relational test (Chapter 3)

Repeat condition

Repeats a group of commands until condition is true; condition is

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tested when the End instruction is encountered Menu(item#,"title1", label1ã,item#, "title2",label2,...ä)

Sets up branching within a program as selected from menu keys & through *; when encountered, displays the first of up to 3 menu groups (up to 15 titles); when you select a title, the program branches to the label that the title represents; item# is an integer ‚ 1 and  15 that specifies title’s menu placement; title is a text string from one to eight characters long (may be abbreviated in the menu)

Lbl label

Assigns a label to a program command; label can be one to eight characters long, starting with a letter

Goto label

Transfers control to the program branch labeled with label

IS>(variable,value)

Adds 1 to variable; if the answer is > value, the next command is skipped; if the answer is  value, the next command is executed; variable cannot be a built-in variable

DS<(variable,value)

Subtracts 1 from variable; if the answer is < value, the next command is skipped; if the answer is ‚ value, the next command is executed; variable cannot be a built-in variable

Pause

Halts the program so that you can examine results, including displayed graphs and tables; to resume the program, press b

Pause value

Displays value on the home screen so that you can scroll large values, such as lists, vectors, or matrices; to resume, press b

Return

Exits a subroutine (page 224) and returns to the calling program, even if encountered within nested loops; within the main program, stops the program and returns to the home screen (an implied Return exits each subroutine upon completion and returns to the calling program)

Stop

Stops a program and returns to the home screen

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Chapter 16: Programming

A command line that is longer than the screen is wide automatically continues at the beginning of the next line.

DelVar(variable)

Deletes from memory variable (except program names) and its contents

GrStl(function#,graphStyle#)

Specifies the graph style represented by graphStyle# for the function represented by function#; function# is the number part of an equation variable, such as the 5 in y5; graphStyle# is an integer ‚ 1 and  7, where 1 = » (line), 2 = ¼ (thick), 3 = ¾ (shade above), 4 = ¿ (shade below), 5 = À (path), 6 = Á (animate), and 7 =  (dotted)

*LCust(item#,"title" ã,item#,"title",...ä)

Loads (defines) the TI-86 custom menu, which is displayed when you press 9; item# is an integer ‚ 1 and  15; title is a string with one to eight characters (may be abbreviated in the menu)

Entering a Command Line You can enter on a command line any instruction or expression that you could execute on the home screen. In the program editor, each new command line begins with a colon. To enter more than one instruction or expression on a single command line, separate each with a colon. To move the cursor down to the next new command line, press b. You cannot move to the next new command line by pressing #. However, you can return to existing command lines to edit them by pressing $.

All CATALOG items are valid in the program editor.

Menus and Screens in the Program Editor TI-86 menus and screens may be altered when displayed in the program editor. Menu items that are invalid for a program are omitted from menus. Menus that are not valid in a program, such as the LINK menu or MEM menu, are not displayed at all. When you select a setting from a screen such as the mode screen or graph format screen, the setting you select is pasted to the cursor location on the command line.

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Variables to which you typically store values from an editor, such as the window variables, become items on program-only menus, such as the GRAPH WIND menu. When you select them, they are pasted to the cursor location on the command line.

Running a Program To resume the program after a pause, press b.



Paste the program name to the home screen. Either select it from the PRGM NAMES menu (8 &) or enter individual characters.



Press b. The program begins to run.

Each result updates the last-answer variable Ans (Chapter 1). The TI-86 reports errors as the program runs. Commands executed during a program do not update the previous-entry storage area ENTRY (Chapter 1). The example program below is shown as it would appear on a TI-86 screen. The program: ♦ Creates a table by evaluating a function, its first derivative, and its second derivative at intervals in the graphing window ♦ Displays the graph of the function and its derivatives in three different graph styles, activates the trace cursor, and pauses to allow you to trace the function

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Chapter 16: Programming PROGRAM:FUNCTABL :Func:Fix 2:FnOff:PlO ff :y1=.6 x cos x :ClLCD :Eq4St(y1,STRING) :Outpt(1,1,"y1=") :Outpt(1,4,STRING) :Outpt(8,1,"PRESS ENT ER") :Pause :ClLCD :y2=der1(y1,x,x) :y3=der2(y1,x,x) :DispT :GrStl(1,1):GrStl(2,2 ):GrStl(3,7) :2¶xRes :ZTrig :Trace

The name of the program Set graphing and decimal modes (mode screen); turn off functions (GRAPH VARS menu) and plots (STAT PLOT menu) Define the function (assignment statement) Clear the home screen (PRGM IàO menu) Convert y1 into the string variable STRING (STRNG menu) Display y1= at row 1, column 1 (PRGM IàO menu) Display value stored to STRING at row 1, col. 4 (PRGM IàO menu) Display PRESS ENTER at line 8, column 1 (PRGM IàO menu) Pause the program (PRGM CTL menu) Clear the home screen (PRGM IàO menu) Define y2 as the first derivative of y1 (CALC menu) Define y3 as the second derivative of y1 (CALC menu) Display the table (PRGM IàO menu) Set graph styles for y1, y2, and y3 (PRGM CTL menu) Store 2 to the window variable xRes (GRAPH WIND menu) Set the viewing window variables (GRAPH ZOOM menu) Display the graph, activate trace cursor, and pause (GRAPH menu)

Breaking (Interrupting) a Program To break (interrupt) the program, press ^. The ERROR 06 BREAK menu is displayed. ♦ To display the program editor where the interruption occurred, select GOTO (&). ♦ To return to the home screen, select QUIT (*).

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Working with Programs Managing Memory and Deleting a Program To check whether adequate memory is available for a program you want to enter or download, display the Check RAM screen (- ™ &; Chapter 17). To increase available memory, consider deleting selected items or data types from memory (Chapter 17). Editing a Program After you write a program, you can display it in the program editor and edit any command line. The program editor does not display a $ to indicate that command lines continue beyond the screen.



Display the program editor (8 '). The PRGM NAMES menu also is displayed.



Enter the name of the program you want to edit. Either select the name from the PRGM NAMES menu or enter the individual characters.



Edit the program command lines. Move the cursor to the appropriate location, and then delete, overwrite, or insert characters. Press : to clear the entire command line, except for the leading colon, and then enter a new program command. ♦ Select program editor menu items INSc (*) and DELc (/ &) to insert and delete command lines.

♦ ♦

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Calling a Program from Another Program On the TI-86, any stored program can be called from another program as a subroutine. In the program editor, enter the subroutine program name on a command line by itself. ♦ Press 8 to display the PRGM NAMES menu, and then select the program name. ♦ Use ALPHA keys and alpha keys to enter the program name’s individual characters. When the program name is encountered as the calling program runs, the next command executed is the first command in the subroutine. It returns to the next command in the calling program when it encounters Return (or implied Return) at the end of a subroutine. Calling program

InputàOutput

Subroutine

label used with Goto and Lbl is local to the program where it is located. label in one program is not recognized by another program. You cannot use Goto to branch to a label in another program.

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Copying a Program to Another Program Name

Display a new or existing program in the program editor.



Move the cursor to the command line on which you want to copy a program.



Display the Rcl prompt (- –).



Enter the name of the program you want to copy. Either select the name from the PRGM NAMES menu or enter individual characters.



Press b. The contents of the recalled program name are inserted into the other program at the cursor location.

Using and Deleting Variables within a Single Program If you want to use variables within a program but do not need them after the program is run, you can use DelVar( within the program to delete the variables from memory. The program segment to the right uses the variables A and B as counters and then deletes them from memory.

:3¶B :For (A,1,100,1) :B+A¶B :End :Disp A :Disp B :DelVar(A) :DelVar(B)

Running an Assembly Language Program An assembly language program is a program that runs much faster and has greater control of the calculator than the regular programs described in this chapter. You can download and run TI-created assembly language programs to add features to your TI-86 that are not built in. For example, you can download the TI-83 finance or inferential statistics features to use on your TI-86.

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Chapter 16: Programming

TI assembly language programs and other programs are available on TI’s World Wide Web site: http:ààwww.ti.comàcalc

When you download an assembly language program, it is stored among the other programs as a PRGM NAMES menu item. You can: ♦ Transmit it using the TI-86 communication link (Chapter 18). ♦ Delete it using the MEM DELETE:PRGM screen (Chapter 17). ♦ Call it from another program as a subroutine (page 224). To run an assemblyProgramName, the syntax is: Asm(assemblyProgramName) If you write an assembly language program, use the two instructions below from the CATALOG. AsmComp(AsciiAssemblyPrgmName, HexAssemblyPrgmName)

Compiles an assembly language program written in ASCII and stores the hex version

AsmPrgm

Identifies an assembly language program; must be entered as the first line of an assembly language program

Entering and Storing a String A string is a sequence of characters that you enclose within quotation marks. ♦ A string defines characters to be displayed in a program. ♦ A string accepts input from the keyboard in a program. You do not use quotation marks to enter a string name. In concatenation, you can substitute stringName for any "string".

To enter a string directly, the syntax is: "string" To concatenate (join together) two or more strings, use \. The syntax is: "stringA"+"stringB"+"stringC"+...

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The STRNG (String) Menu "

sub

lngth

227

-“ Eq4St

St4Eq

" also marks the start and

"string"

Marks the start and end of string

end of a formula to be attached to a list; it is also an item on the list editor menu (Chapter 11).

sub("string",begin,length) sub(stringName,begin,length)

Returns a subset of "string" or stringName, starting at begin character place and length characters long

lngth "string" or lngth stringName

Returns the number of characters in "string" or stringName

Eq4St(equationVariable,stringName)

Converts equationVariable contents to stringName

St4Eq(stringName,equationVariable)

Converts stringName to equationVariable

Creating a String Begin these steps on a blank line on the home screen or in the program editor.



Display the STRNG menu.

-“



Enter the open quotation mark, then the string SOLVE & GRAPH, and then the close quotation mark.

&11 ãSä ãOä ãLä ãVä ãEä ¤ - Ÿ&(¤ ãGä ãRä ãAä ãPä ãHä -“&

To evaluate the contents of a string, you must use St4Eq( to convert it to an equation.



Store the string to the string variable name LABEL.

1X ãLä ãAä ãBä ãEä ãLä b

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17

Memory Management TI-86

Checking Available Memory ............................................ 230 Deleting Items from Memory ........................................... 231 Resetting the TI-86 .......................................................... 232

M1

M2

M3

M4

M5

F1

F2

F3

F4

F5

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Chapter 17: Memory Management

Checking Available Memory The MEM (Memory) Menu For information on TOL (the tolerance editor), refer to the Appendix.

RAM

DELET RESET

-™ TOL

ClrEnt

check-RAM memory/default clears ENTRY screen reset menu storage area memory delete tolerance menu editor

Checking Memory Usage - ™ & When all memory is cleared and all defaults are set, the standard TI-86 has 98,224 bytes of available random-access memory (RAM). As you store information to RAM, you can monitor memory allocation on the Check RAM screen. MEM FREE reports the total number of bytes available in RAM. Conversely, all other numbers on the screen report the number of bytes that each data type currently occupies. For example, if you were to store a 50-byte matrix in memory, the MATR total would increase to 50 bytes, while the MEM FREE total would decrease by 50 to 98174 bytes.

To display the number of bytes that a specific variable occupies, display the DELETE screen for that data type (page 231). Scroll the screen, if necessary.

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Deleting Items from Memory The MEM DELET (Delete) Menu ALL

REAL

CPLX

LIST

-™' VECTR

4 4

MATRX STRNG GDB

EQU

CONS

PRGM

PIC

To delete a parametric equation, delete the xt component.

Each MEM DELET menu item displays the deletion screen for that data type. For example, when you select LIST, the MEM DELETE:LIST screen is displayed. Use the DELETE screens to delete any user-created variable and the information stored to it.

In the example, the equation



Select DELET from the MEM menu to display the MEM DELET menu.

-™'



Select the data type of the item you want to delete. To scroll down to the next six items or up to the previous six items, select PAGE$ or PAGE#.

/(



Move the selection cursor ( 4 ) to the item you want to delete (y5). The uppercase items are in alphanumeric order, followed by the lowercase items in alphanumeric order.

###



Delete the item. To delete other items on the screen, repeat steps 3 and 4.

b

y5=x^3Nx 2+4xN1 is deleted.

To move directly to the first item beginning with any letter, enter that letter; ALPHA-lock is on.

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Chapter 17: Memory Management

Resetting the TI-86 The MEM RESET (Reset) Menu Before resetting all memory, consider deleting selected information to increase memory capacity (page 231).

When you select and confirm ALL or DFLTS, the default

contrast is reset; to adjust it, use - $ or - # (Chapter 1).

RAM ALL

DELET RESET MEM DFLTS

TOL

-™( ClrEnt

ALL

When confirmed, all data is cleared and memory is reset; both messages are displayed

MEM

When confirmed, clears all stored data from memory; Mem Cleared is displayed

DFLTS

When confirmed, resets all defaults; Defaults Set is displayed

When you select ALL, MEM, or DFLTS, a confirmation menu is displayed. ♦ To confirm the selected reset, select YES (press )). ♦ To cancel the selected reset, select NO (press *).

ClrEnt (Clear Entry) - ™ * The TI-86 retains as many previous entries as possible in ENTRY, up to a capacity of 128 bytes. To clear the ENTRY storage area of all entries, execute ClrEnt on a blank line on the home screen (- ™ * b).

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18

The TI-86 Communication Link TI-86

TI-86 Linking Options ...................................................... 234 Connecting the TI-86 to Another Device ......................... 235 Selecting Data to Send..................................................... 236 Preparing the Receiving Device ....................................... 240 Transmitting Data ............................................................ 240 Receiving Transmitted Data............................................. 240

M1

M2

M3

M4

M5

F1

F2

F3

F4

F5

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Chapter 18: The TI-86 Communication Link

TI-86 Linking Options Using the unit-to-unit cable included with the TI-86, you can transmit data between the TI-86 and several other devices. Linking Two TI-86s You can link two TI-86 units and select the data types to be transmitted, including programs. You can back up the entire memory of a TI-86 onto another TI-86. Linking a TI-86 and a TI-85 You can select the data types, including programs, to transfer from a TI-85 to a TI-86. You can send most variables and programs from a TI-86 to a TI-85 using SND85 (page 239), except lists, vectors, or matrices that exceed TI-85 capacity. When you run a TI-85 program on a TI-86, the TI-85 PrtScrn program instruction is not valid. Also, the EOS implied multiplication on the TI-86 differs from the TI-85 (Appendix). For example, the TI-85 interprets sin 2x as sin (2x); the TI-86 interprets sin 2x as (sin 2)x. Linking a TI-86 and a CBL 2/CBL or CBR System The Calculator-Based Laboratoryé (CBL 2é/CBLé) and Calculator-Based Rangeré (CBRé) systems are optional TI accessories that collect data from physical occurrences, such as science experiments. The CBL 2/CBL and CBR store data to lists, which you can transmit to a TI-86 and analyze. You can transmit list names to a CBL 2/CBL or CBR from a TI-86.

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Linking a TI-86 and a PC or Macintosh TI-86 TI-GRAPH LINKè is an optional system that links a TI-86 with an IBMê-compatible or Macintoshê computer. Downloading Programs from the Internet If you have TI-GRAPH LINK and internet services, you can download programs from TI’s World Wide Web site at: http:ààwww.ti.comàcalc

You can download various programs from TI’s web site, including assembly language programs that add features such as TI-83 finance and inferential statistics. The site also links to many other TI-86 web sites maintained by user groups, high schools, universities, and individuals.

Connecting the TI-86 to Another Device Before you begin to transmit data to or from the TI-86, connect it to the other device.

Firmly insert one end of the unit-to-unit cable into the port on the bottom edge of the calculator.



Firmly insert the other end of the cable into the other device (or PC adapter).

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Chapter 18: The TI-86 Communication Link

The LINK Menu SEND The link menus are not available in the program editor.

RECV

-o SND85

menu of data menu of data types types to send to send to a TI-85 receive mode (waiting)

Selecting Data to Send The CBL 2/CBL, CBR, and TI-86 TI-GRAPH LINK have built-in Silent Link, which eliminates the need for you to set up the devices to send or receive.

To list the variables for a specific data type on a selection screen, select the data type from the LINK SEND menu. When you select BCKUP, the message Memory Backup is displayed. The LINK SEND Menu memory backup

-o& all real and complex data types

matrices programs

graph databases

BCKUP PRGM MATRX

GDB

vectors lists

ALL

complex values in all data types real values in all data types equations

4

LIST

VECTR

REAL

CPLX

4

CONS

PIC

WIND

STRNG

window variable values

strings

user-created constants pictures

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EQU

Chapter 18: The TI-86 Communication Link

237

Initiating a Memory Backup To initiate a memory backup, select BCKUP from the LINK SEND menu (- o & &). The screen to the right is displayed. To complete memory backup, prepare the other unit to receive data transmission (page 239), and then select XMIT from the memory backup menu (&). Warning: When you transmit BCKUP, the transmitted memory overwrites all memory in the receiving unit; all information in the memory of the receiving unit is lost. To cancel initiation of a memory backup, press .. If a transmission error occurs during a backup, the receiving-calculator memory is reset.

As a safety check to prevent accidental loss of memory, when the receiving calculator is notified of an incoming backup transmission, it displays the warning message and confirmation menu, as shown in the screen to the right. ♦ To continue the backup transmission, select CONT. The backup transmission continues, replacing all receiving-calculator memory with the backup data. ♦ To cancel backup and retain all receiving-calculator memory, select EXIT. Selecting Variables to Send

If no data of the type you select is stored in memory, the message is displayed: NO VARS OF THIS TYPE.

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Chapter 18: The TI-86 Communication Link

When you select any LINK SEND menu item, except BCKUP or WIND, each variable of the selected data type is listed in alphanumeric order on a selection screen. The screen to the right is the SEND ALL screen (- o & *). ♦ The data type of each variable is specified. ♦ Small squares indicate that xStat, yStat, and Q2 are selected to be sent. ♦ The selection cursor is next to Q4. To select a specific variable to be sent, use # and $ to move the selection cursor next to the variable, and then select SELCT (') from the selection screen menu. ♦ To select all variables of this type, select ALL+ from the selection screen menu ((). ♦ To deselect all variables of this type, select ALL- from the selection screen menu ()). To complete transmission of the selected variables, prepare the other unit to receive data transmission (page 239), and then select XMIT from the selection screen menu (&). The SEND WIND (Window Variables) Screen When you select WIND from the LINK SEND menu (- o & / / (), the SEND WIND screen is displayed. Each SEND WIND screen item represents the window variables, format settings, and any other graph-screen data for that TI-86 graphing mode and for ZRCL (user-created zoom). The screen to the right shows that the graph screen data for Func and DifEq graphing modes are selected. Func

Select to send Func graphing mode window variable values and format settings

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Pol

Select to send Pol graphing mode window variable values and format settings

Param

Select to send Param graphing mode window variable values and format settings

DifEq

Select to send DifEq graphing mode window variable values, difTol, axes settings, and format settings

ZRCL

Select to send user-created zoom window variables, and format settings in any mode

To complete transmission of the selected variables, prepare the other unit to receive data transmission (below), and then select XMIT from the memory backup menu (&). Sending Variables to a TI-85 The steps for selecting variables to send to a TI-85 are the same as those for selecting variables to send to a TI-86. However, the LINK SND85 menu has fewer items than the LINK SEND menu. The TI-86 has more capacity for lists, vectors, and matrices than the TI-85. If you send to the TI-85 a list, vector, or matrix that has more elements than the TI-85 allows, the elements that exceed TI-85 capacity are truncated. The LINK SND85 (Send Data to TI-85) Menu MATRX

LIST

VECTR

REAL

CPLX

-o( 4

CONS

PIC

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STRNG

240

Chapter 18: The TI-86 Communication Link

Preparing the Receiving Device To prepare a PC to receive data, consult the TI-GRAPH LINK guidebook.

To prepare a TI-86 or TI-85 to receive data transmission, select RECV from the LINK menu (- o '). The message Waiting and the busy indicator are displayed. The calculator is ready to receive transmitted items. To cancel receive mode without receiving items, press ^. When the LINK TRANSMISSION ERROR message is displayed, select EXIT from the menu (&). The LINK menu is displayed.

Transmitting Data After you select data types on the sending unit and prepare the receiving unit to receive data, you can begin transmitting. To begin transmitting, select XMIT on the selection screen menu of the sending calculator (&). To interrupt transmission, press ^ on either calculator. When the LINK TRANSMISSION ERROR message is displayed, select EXIT from the menu (&). The LINK menu is displayed.

Receiving Transmitted Data As the TI-86 receives transmitted data, each variable name and data type is displayed line by line. If all selected items are transmitted successfully, the message Done is displayed. To scroll the transmitted variables, press # and $.

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During transmission, if a transmitted variable name is stored already in the memory of the receiving calculator, transmission is interrupted. The duplicated variable name, its data type, and the DUPLICATE NAME menu are displayed, as shown in the screen to the right. To resume or cancel transmission, you must select an item from the DUPLICATE NAME menu. RENAM

Displays the Name= prompt; enter a unique variable name; press b to continue transmission

OVERW

(overwrite) Replaces data stored to the receiving unit’s variable with sent variable data

SKIP

Does not overwrite the receiving unit’s data; attempts to send the next selected variable

EXIT

Cancels the data transmission

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Chapter 18: The TI-86 Communication Link

Repeating Transmission to Several Devices After transmission is complete, the LINK menu is displayed and all selections remain. You can transmit the same selections to a different TI-86 without having to re-select data. To repeat a transmission with another device, disconnect the unit-to-unit cable from the receiving unit; connect it to another device; prepare the device to receive data; and then select SEND, then ALL, and then XMIT.

If the cable is connected but a transmission error occurs, push the cable in more firmly to both calculators and try again.

Error Conditions A transmission error occurs after a few seconds if: ♦ The cable is not connected to the port of the sending calculator. ♦ The cable is not connected to the port of the receiving calculator. ♦ The receiving unit is not set to receive transmission. ♦ You attempt a backup between a TI-86 and a TI-85. Insufficient Memory in Receiving Unit If the receiving unit does not have sufficient memory to receive an item, the receiving unit displays LINK MEMORY FULL and the variable name and data type. ♦ To skip the variable, select SKIP. Transmission resumes with the next item. ♦ To cancel transmission altogether, select EXIT.

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19

Applications TI-86

Using Math Operations with Matrices ............................. 244 Finding the Area between Curves.................................... 245 The Fundamental Theorem of Calculus............................ 246 Electrical Circuits.............................................................. 248 Program: Taylor Series ..................................................... 250 Characteristic Polynomial and Eigenvalues...................... 252 Convergence of the Power Series .................................... 254 Reservoir Problem............................................................ 256 Predator-Prey Model........................................................ 258 Program: Sierpinski Triangle ............................................ 260

M1

M2

M3

M4

M5

F1

F2

F3

F4

F5

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Chapter 19: Applications

Using Math Operations with Matrices

Displaying the result matrix elements to 11 decimal places illustrates accuracy.



In the matrix editor, enter matrix A as shown.



On the home screen, select rref from the MATRX OPS menu.



To append a 3×3 identity matrix to matrix A, select aug from the MATRX OPS menu, enter A, select ident from the MATRX OPS menu, and then enter 3. Execute the expression.



Enter Ans (to which the matrix from step 3 is stored). Define a submatrix that contains the solution portion of the result. The submatrix begins at element (1,4) and ends at element (3,6).



Select 4Frac from the MATH MISC menu and display the fractional equivalent of the submatrix.



Check the result. Set the decimal mode to 11 (the last 1) Select round from the MATH NUM menu for the product of the fractional equivalent of the submatrix times A.

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Finding the Area between Curves Find the area of the region bounded by:

If necessary, select ALLfrom the equation editor menu to deselect all functions. Also, turn off all stat plots.

In Func graphing mode, select y(x)= from the GRAPH menu to display the equation editor and enter the equations as shown. y1=300 xà(x 2+625)



f(x)=300 xà(x 2+625) g(x)=3 cos (.1 x) x=75

y2=3 cos (.1 x)

Select WIND from the GRAPH menu and set the window variables as shown. xMin=0

xMax=100

xScl=10

yMin=L5

yMax=10

yScl=1

xRes=1



Select GRAPH from the GRAPH menu to display the graph screen.



Select ISECT from the GRAPH MATH menu. Move the trace cursor to the intersection of the functions. Press b to select y1. The cursor moves to y2. Press b. Then press b again to set the current cursor location as the initial guess. The solution uses the solver. The value of x at the intersection, which is the lower limit of the integral, is stored to Ans and x.



The area to integrate is between y1 and y2, from x=5.5689088189 to x=75. To see the area on a graph, return to the home screen, select Shade from the GRAPH DRAW menu, and execute this expression: Shade(y2,y1,Ans,75)



Select TOL from the MEM menu and set tol=1EL5.



On the home screen, compute the integral with fnInt (CALC menu). The area is 325.839961998. fnInt(y1Ny2,x,Ans,75)

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The Fundamental Theorem of Calculus If necessary, select ALLfrom the equation editor menu to deselect all functions. Also, turn off all stat plots.

Consider these three functions: F(x)1 = (sin x)àx

In the example, nDer(y2,x) only approximates y3; you cannot define y3 as der1(y2,x).

F(x) 3 =

d dx

x

‰0

(sin t)àt dt

In Func graphing mode, select y(x)= from the GRAPH menu, and then enter the functions and set graph styles in the equation editor as shown. (fnInt and nDer are CALC menu items.) Ây1=(sin x)àx



x

F(x)2 = ‰0 (sin t)àt

»y2=fnInt(y1(t),t,0,x)

¼y3=nDer(y2,x)

Select TOL from the MEM menu to display the tolerance editor. To improve the rate of the calculations, set tol=0.1 and d=0.001.

Select WIND from the GRAPH menu and set the window variable values as shown. xMin=L10

xMax=10

xScl=1

yMin=L2.5

yMax=2.5



Select TRACE from the GRAPH menu to display the graph and the trace cursor.



Trace y1 and y3 to verify that the graph of y1 and the graph of y3 are visually indistinguishable.

yScl=1

xRes=4

The inability to visually distinguish between the graphs of y1 and y3 graphically supports the fact that:

d dx

x

‰0

(sin t)àt dt = (sin x)àx

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Chapter 19: Applications

Deselect y2 in the equation editor.



Select TBLST from the TABLE menu. Set TblStart=1, @Tbl=1, and Indpnt: Auto.



Select TABLE from the TABLE menu to display the table. Compare the solution of y1 with the solution of y3 to numerically support the formula above.

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Chapter 19: Applications

Electrical Circuits A measurement device has measured the DC current (C) in milliamperes and voltage (V) in volts on an unknown circuit. From these measurements, you can calculate power (P) in milliwatts using the equation CV=P. What is the average of the measured power? With the TI-86, you can estimate the power in milliwatts at a current of 125 milliamperes using the trace cursor, the interpolateàextrapolate editor, and a regression forecast.

In two consecutive columns of the list editor, store the current measurements shown below to the list name CURR and the voltage measurements shown below to the list name VOLT. {10,20,40,60,80,100,120,140,160}¶CURR {2,4.2,10,18,32.8,56,73.2,98,136}¶VOLT



In the next column of the list editor, enter the list name POWER .



Enter the formula CURR ¹VOLT in the list editor entry line for POWER. Press b to calculate the values for power and store the answers to the list name POWER.



Select WIND from the GRAPH menu and set the window variable values as shown. xMin=0



xMax=max(POWER) xScl=1000 yMin= 0

yMax=max(CURR) yScl=10

From the home screen, select FnOff from the CATALOG and press b to deselect all functions in the equation editor. Select Plot1( from the CATALOG and set up a stat plot with POWER on the x-axis and CURR on the y-axis.

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Chapter 19: Applications

The 7s and 8s in parentheses specify the 7th and 8th elements of POWER and CURR.

To enter each regression after LinR, press - ¢ and edit as needed.



Select TRACE from the GRAPH menu to display the stat plot and trace cursor on the graph screen.



Trace the stat plot to approximate the value of POWER at CURR=125. With this statistical data, the closest to CURR=125 that you can trace to is CURR=120 (on the y-axis).



Select INTER from the MATH menu to display the interpolateàextrapolate editor. To interpolate POWER at CURR=125, enter the nearest pairs: x1=POWER(7) x2=POWER(8)

249

y1=CURR(7) y2=CURR(8)



Enter y=125 and solve for x.



On the home screen, select LinR from the STAT CALC menu to fit the linear regression model equation to the data stored to POWER and CURR. Write down the value of the result variable corr.



Fit the logarithmic (LnR), exponential (ExpR), and power (PwrR) regressions to the data, writing down the value of corr for each regression. Compare the corr values of each regression to determine which model fits the data most accurately (the corr value closest to 1).



Execute the most accurate regression again, and then select FCST from the STAT menu. To forecast POWER at CURR=125, enter y=125 and solve for x.

Compare this answer with the answer returned in step 9.

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Program: Taylor Series When you run this program, you can enter a function and specify the order and center point. Then the program calculates the Taylor Series approximation for the function and plots the function you entered. This example shows how to call a program from another program as a subroutine.

Before you enter the program TAYLOR, select EDIT from the PRGM menu, enter MOBIUS at the Name= prompt, and then enter this brief program to store the Mobius Series. The program TAYLOR calls this program and runs it as a subroutine. PROGRAM:MOBIUS :{1,L1,L1,0,L1,1,L1,0,0,1,L1,0,L1,1,1,0,L1,0,L1,0}¶MSERIES :Return

The higher-order derivative values necessary for this program are calculated numerically based on the methods in “Numerical Differentiation of Analytic Functions,” J. N. Lyness and C. B. Moler, SIAM Journal of Numerical Analysis 4 (1967): 202-210.

Select EDIT from the PRGM menu, enter TAYLOR at the Name= prompt, and then enter this program to calculate the Taylor Series.

H is on the CHAR GREEK menu

User enters equation function User enters order User enters center

PROGRAM:TAYLOR :Func:FnOff :y14=pEval(TPOLY,xNcenter) :GrStl(14,2) :1EL9¶H:.1¶rr :ClLCD :InpSt "FUNCTION: ",EQ :St8Eq(EQ,y13) :Input "ORDER: ",order :order+1¶dimL TPOLY :Fill(0,TPOLY) :Input "CENTER: ",center :evalF(y13,x,center)¶f0 :f0¶TPOLY(order+1)

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Chapter 19: Applications

Begins Then group Calls subroutine Begins For group Begins While group Creates nested While group

Creates nested For group

Ends While group Ends For group Ends Then group

:If order‚1 :der1(y13,x,center)¶TPOLY(order) :If order‚2 :der2(y13,x,center)à2¶TPOLY(orderN1) :If order‚3 :Then :MOBIUS :For(N,3,order,1) :abs f0¶gmax:gmax¶bmi :1¶m:0¶ssum :While abs bmi‚H¹gmax :While MSERIES(m)==0 :m+1¶m :End :0¶bsum :For(J,1,m¹N,1) :rr¹e^(2p(Jà(m¹N))¹(0,1))+(center,0)¶x :real y13¶gval :bsum+gval¶bsum :max(abs gval,gmax)¶gmax :End :bsumà(m¹N)Nf0¶bmi :ssum+MSERIES(m)¹bmi¶ssum :m+1¶m :End :ssumà(rr^N)¶TPOLY(order+1NN) :End :End :ZStd

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On the home screen, select TAYLOR from the PRGM NAMES menu, and then press b to run the program.



When prompted, enter: FUNCTION: sin x ORDER: 5 CENTER: 0

Characteristic Polynomial and Eigenvalues

In the matrix editor or on the home screen, enter matrix A as shown. [[L1,2,5][3,L6,9][2,L5,7]]¶A

The first eigenvalue is real, since the imaginary part is 0. If necessary, select ALLfrom the equation editor menu to deselect all functions. Also, turn off all stat plots.



On the home screen, select eigVl from the MATRX MATH menu to find the complex eigenvalues for the matrix A and store them to the list name EV.



Graph the characteristic polynomial Cp(x) of matrix A without knowing the analytic form of Cp(x) based on the formula Cp(x)=det(ANx¹I). In Func graphing mode, select y(x)= from the GRAPH menu and enter the function in the equation editor as shown. »y1=det (ANx¹ident 3)



Select WIND from the GRAPH menu and set the window variable values as shown. xMin=L10



xMax=10

xScl=1

yMin=L100

yMax=50

Select ROOT from the GRAPH MATH menu and use it to display the real eigenvalue interactively. Use Left Bound=L5, Right Bound=L4, and Guess=L4.5. Compare the root (x value) you displayed interactively with the first element of the result list in step 2.

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Next, use the list editor and a degree-three polynomial regression to find an analytic formula in terms of x for the characteristic polynomial y1=det(ANx¹ident 3). Create two lists that you can use to find the analytic formula.

To clear the menus from the graph screen, press :.



In the list editor, create elements for xStat by entering the expression seq(N,N,L10,21) in the xStat entry line. seq is on the MATH MISC menu.



Create elements for yStat by attaching the formula "y1(xStat)" to yStat in the entry line. The expression is evaluated when you press b or exit the list editor.



On the home screen, select Plot1( from the CATALOG and execute Plot1(2,xStat,yStat,1) to turn on Plot1 as an xyLine plot using the lists xStat and yStat.



Select GRAPH from the GRAPH menu to display Plot1 and y1 on the graph screen.



On the home screen, select P3Reg from the STAT CALC menu. Execute P3Reg xStat,yStat,y2 to find the explicit characteristic polynomial in terms of x and store it to y2. The cubic regression coefficients stored in the result list PRegC suggest that a=L1, b=0, c=14, and d=L24. So the characteristic polynomial seems to be Cp(x)=Lx 3+14xN24.

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Chapter 19: Applications 쐈

Support this conjecture by graphing y1, y2 (to which Cp(x) is stored), and Plot1 together.



In the equation editor, enter the apparent characteristic polynomial of matrix A and select ¼ (thick) graph style as shown. ¼y3=Lx^3+14xN24



Graph y1, y2, y3, and Plot1.



Deselect y2 in the equation editor.



Select TABLE from the TABLE menu to display y1 and y3 in the table. Compare the values for the characteristic polynomial.

Convergence of the Power Series A closed-form analytic antiderivative of (sin x)àx does not exist. However, substituting t for x, you can find an infinite series analytic solution by taking the series definition of sin t, dividing each term of the series by t, and then integrating term by term to yield: ˆ

G L1

n+1 2nN1à((2n

t

N1)(2n N1)!)

n=1

Plot finite approximations of this power series solution on the TI-86 with sum and seq.

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Chapter 19: Applications

If necessary, select ALLN from the equation editor menu to deselect all functions. Also, turn off all stat plots.



Select TOL from the MEM menu and set tol=1.



On the mode screen, set Radian angle mode and Param graphing mode.



In the equation editor, enter the parametric equations for the power series approximation as shown. Select sum and seq from the LIST OPS menu. Select ! from the MATH PROB menu. »xt1=t



This example is set up in



To clear the menus from the graph screen, press :.

yt2=fnInt((sin w)àw,w,0,t)

Select WIND from the GRAPH menu and set the window variable values as shown. tMin=L15 tMax=15 tStep=0.5

you to control the solution with tStep and increase plotting speed.

yt1=sum seq((L1)^(j+1)t^(2jN1)à((2jN1)(2jN1)!),j,1,10,1)

In the equation editor, enter the parametric equations as shown to plot the antiderivative of (sin x)àx and compare it with the plot of the power series approximation. (Select fnInt from the CALC menu.) ¼xt2=t

Param mode, which allows

255

xMin=L15 xMax=15 xScl=1

yMin=L3 yMax=3 yScl=1



Select FORMT from the GRAPH menu and set SimulG format.



Select GRAPH from the GRAPH menu to plot the parametric equations on the graph screen.



In the equation editor, modify yt1 to compute the first 16 terms of the power series by changing 10 to 16. Plot the equations again. In this example, the window variable tStep controls the plotting speed. Select WIND from the GRAPH menu and set tStep=1 and observe the difference in plotting speed and curve smoothness.

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Reservoir Problem On the TI-86, you can use parametric graphing animation to solve a problem. Consider a water reservoir with a height of 2 meters. You must install a small valve on the side of the reservoir such that water spraying from the open valve hits the ground as far away from the reservoir as possible. At what height should you install the valve to maximize the length of the water stream when the valve is wide open? Assume a full tank at time=0, no acceleration in the x direction, and no initial velocity in the y direction. Also, ignore valve-size and valve-type factors. Integrating the definition of acceleration in both the x and y directions twice yields the equations x=v0t and y=h0N(gt2)à2. Solving Bernoulli’s equation for v0 and substituting into v0t results in this pair of parametric equations: xt=t‡(2g(2Nh0))

yt=h0N(gt2)à2

t = time in seconds h0 = height of the valve in meters g = the built-in acceleration of gravity constant When you graph these equations on the TI-86, the y-axis (x=0) is the side of the reservoir where the valve is to be installed. The x-axis (y=0) is the ground. Each plotted parametric equation represents the water stream when the valve is at each of several heights.

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Chapter 19: Applications If necessary, select ALLN from the equation editor menu to deselect all functions. Also, turn off all stat plots.

To clear the menus from the graph screen, press :.



257

In Param graphing mode, select E(t)= from the GRAPH menu and enter the equations in the equation editor as shown. This pair of equations plots the path of the water stream when the valve is installed at a height of 0.5 meters. »xt1=t‡(2g(2N0.5))

yt1=0.5N(g¹t 2)à2



Move the cursor to xt2=. Press - – ' 1 1, and press b to recall the contents of xt1 into xt2. For xt2, change the valve height (which is 0.5) to 0.75 meters. Do the same with yt1 and yt2.



Repeat step 3 to create three more pairs of equations. Change the valve height to 1.0 meters for xt3 and yt3, 1.5 meters for xt4 and yt4, and 1.75 meters for xt5 and yt5.



Select WIND from the GRAPH menu and set the window variable values as shown. tMin=0 xMin=0 yMin=0 tMax=‡(4àg) xMax=2 yMax=2 tStep=0.01 xScl=0.5 yScl=0.5



Select FORMT from the GRAPH menu and set SimulG graph format.



Select GRAPH from the GRAPH menu to plot the trajectory of the water jets from the five specified heights. Which height seems to create the longest water stream?

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Predator-Prey Model The growth rates of predator and prey populations, such as foxes and rabbits, depend upon the populations of both species. This initial-value problem is a form of the predator-prey model. F'=LF+0.1F¹R

R'=3RNF¹R

Q1 = population of foxes (F) Q2 = population of rabbits (R) Q[1= initial population of foxes (2) Q[2 = initial population of rabbits (5)

Find the population of foxes and rabbits after 3 months (t=3).

In DifEq graphing mode, select Q't= from the GRAPH menu and enter the functions and set graph styles in the equation editor as shown. ¼Q'1=LQ1+0.1Q1¹Q2

»Q'2=3Q2NQ1¹Q2



Select FORMT from the GRAPH menu and set FldOff field format.



Select WIND from the GRAPH menu and set the window variable values as shown. tMin=0 tMax=10 tStep=pà24 tPlot=0



xMin=L1 xMax=10 xScl=5

yMin=L10 yMax=40 yScl=5 difTol=.001

Select INITC from the GRAPH menu and set the initial conditions as shown. tMin=0

Q[1=2

Q[2=5

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Chapter 19: Applications

Select GRAPH from the GRAPH menu to plot the graph of the two populations over time. To see the direction field of the phase-plane solution, select FORMT from the GRAPH screen, and then set DirFld field

format.

Select INITC from the GRAPH menu and delete the values for Q[1 and Q[2.



Select GRAPH from the GRAPH menu to display the direction field of the phase-plane solution.



To see a family of specific phase-plane solutions on top of the direction field, select INITC from the GRAPH menu, and then enter lists for Q[1 and Q[2 as shown. Q[1={2,6,7}

Q[2={6,12,18}



Select TRACE from the GRAPH menu to display the graph with the trace cursor.



Press 3 to see how many foxes and how many rabbits are alive at t=3. (Round the values of Q1 (foxes) and Q2 (rabbits) to whole numbers.) How many foxes and rabbits are alive at t=6? at t=12? On what value of Q1 and Q2 do the phase-plane orbits seem to converge? What is the significance of this value?

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Chapter 19: Applications

Program: Sierpinski Triangle This program creates a drawing of a widely known fractal, the Sierpinski Triangle, and stores the drawing to the picture variable TRI.

Select EDIT from the PRGM menu, enter SIERP at the Name= prompt, and then enter this program.

Sets viewing window Begins For group

IfàThen group

PROGRAM:SIERP :FnOff :ClDrw :PlOff :AxesOff :0¶xMin:1¶xMax :0¶yMin:1¶yMax :rand¶X:rand¶Y :For(K,1,3000) :rand¶N :If N(1 à 3 ) :Then :.5X¶X :.5Y¶Y :End

IfàThen group

IfàThen group Draws point End of For Stores picture

:If N>(1à3) and N(2à3) :Then :.5(.5+X)¶X :.5(1+Y)¶Y :End :If N>(2 à 3 ) :Then :.5(1+X)¶X :.5Y¶Y :End :PtOn(X,Y) :End :StPic TRI



On the home screen, select SIERP from the PRGM NAMES menu and press b to run the program, which may run for several minutes before completion.



After you run the program, you can recall and display the picture by executing RcPic TRI.

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A to Z Function and Instruction Reference TI-86

Quick-Find Locator........................................................... 262 Alphabetical Listing of Operations................................... 266

M1

M2

M3

M4

M5

F1

F2

F3

F4

F5

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Chapter 20: A to Z Function and Instruction Reference

Quick-Find Locator This section lists the TI-86 functions and instructions in functional groups along with the page numbers where they are described in this chapter. Graphing Axes( ................... 271 AxesOff ............... 271 AxesOn................ 271 Circl( .................... 273 ClDrw ................... 273 CoordOff ............. 275 CoordOn.............. 275 DifEq .................... 281 DirFld ................... 282 DrawDot .............. 285 DrawF .................. 286 DrawLine ............. 286 DrEqu( ................. 287

DrInv ....................287 dxDer1 .................288 dxNDer.................288 FldOff ...................295 FnOff ....................296 FnOn ....................297 Func .....................299 GridOff .................301 GridOn .................302 GrStl( ...................302 Horiz ....................304 LabelOff ...............310 LabelOn ...............310

Line( .....................314 Param...................333 Pol ........................336 PolarGC ...............336 PtChg( ..................338 PtOff(....................338 PtOn( ....................338 PxChg( .................340 PxOff( ...................340 PxOn( ...................340 PxTest(.................340 RcGDB .................343 RcPic....................343

RectGC ............... 344 SeqG ................... 351 Shade( ................. 352 SimulG ................ 354 SlpFld .................. 358 StGDB ................. 361 StPic .................... 362 TanLn( ................. 366 Text( .................... 366 Trace ................... 367 Vert ...................... 369 ZData ................... 371 ZDecm ................. 372

ZFit ...................... 373 ZIn........................ 373 ZInt ...................... 374 ZOut .................... 375 ZPrev ................... 375 ZRcl ..................... 376 ZSqr ..................... 376 ZStd ..................... 377 ZTrig .................... 378

SetLEdit .............. 351 sortA ................... 359 sortD ................... 359 Sortx.................... 359

Sorty .................... 359 sum...................... 364 vc4li...................... 369

Lists aug(...................... 270 cSum( .................. 278 Deltalst( ............... 279 dimL..................... 282

¶dimL ..................282 Fill( .......................295 Form( ...................298 List entry: { } .........316

li4vc ......................316 prod......................338 Select( ..................350 seq( ......................351

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Mathematics, Algebra, and Calculus abs ....................... 267 Addition: + ............ 267 and ....................... 268 angle .................... 269 Ans ...................... 269 arc(....................... 269 Assignment: = ...... 270 Ü ........................... 271 Bin ....................... 272 4Bin ...................... 272 ClrEnt .................. 273 ClTbl .................... 273 conj ...................... 275 cos ....................... 276 cos L1 .................... 276 cosh ..................... 277 cosh L1 .................. 277 Þ ........................... 278 Dec....................... 278 4Dec ..................... 279 Degree ................. 279 Degree entry: ¡ ..... 279 der1( .................... 280 der2( .................... 280

Division: / ..............284 DMS entry: ' .........285 4DMS ....................285 dxDer1 .................288 dxNDer.................288 e^ .........................288 Eng.......................290 Eq4St(...................290 Equal: = ................290 Equal to: == ..........291 Euler ....................291 eval ......................291 evalF( ...................292 Exponent: E ..........292 Factorial: ! ............294 Fix ........................295 Float .....................295 fMax( ....................296 fMin( .....................296 fnInt( ....................296 fPart .....................298 4Frac ....................298 gcd( ......................299 Greater than: > .....300

Greater than or equal to: ‚ ..........301 ß ............................302 Hex .......................302 4Hex......................303 imag .....................306 int .........................308 inter(.....................309 Inverse: L1 .............309 iPart......................309 lcm( ......................311 Less than: < ..........312 Less than or equal to:  ..........312 ln ..........................316 log ........................318 max( .....................319 min( ......................320 mod( .....................320 Multiplication: ¹ ....321 nCr .......................322 nDer( ....................323 Negation: L ............323 Normal .................324

not ....................... 325 Not equal to: ƒ ..... 326 nPr ....................... 326 Ý ........................... 326 Oct ....................... 327 4Oct ..................... 327 or ......................... 328 Percent: % ........... 334 pEval( .................. 334 4Pol ...................... 336 PolarC ................. 336 Polar complex:  . 336 poly ..................... 337 Power: ^ .............. 337 Power of 10: 10^ . 337 Radian ................. 341 Radian entry: r ..... 341 real ...................... 343 4Rec ..................... 343 RectC .................. 344 RK........................ 345 Root: x‡ ............... 346 rotL ...................... 347 rotR ..................... 347

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round( ................. 348 Sci........................ 349 shftL .................... 353 shftR .................... 353 sign...................... 354 simult( ................. 354 sin ........................ 355 sin L1 ..................... 355 sinh...................... 356 sinhL1 ................... 356 Solver( ................. 358 Square: 2 .............. 360 Square root: ‡ ...... 360 St4Eq( .................. 361 Store to variable: ¶ ......... 362 Subtraction: N....... 363 tan........................ 364 tan L1 ..................... 365 tanh ..................... 365 tanh L1 ................... 365 xor ....................... 370

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Chapter 20: A to Z Function and Instruction Reference

Matrices aug( ..................... 270 cnorm .................. 273 cond .................... 274 det........................ 281 dim....................... 281

¶dim .................... 281 eigVc ................... 289 eigVl .................... 289 Fill( ...................... 295 ident .................... 304

LU(....................... 318 Matrix entry: [ ] .... 319 mRAdd(............... 321 multR( ................. 322 norm.................... 323

rAdd( ....................340 randM( .................342 ref .........................344 rnorm ...................346 rref .......................348

rSwap( .................348 Transpose: T ........367

Input .....................307 IS>( .......................310 Lbl ........................311 LCust( ..................311 Menu( ...................320 Outpt(...................329 Pause ...................333

Prompt .................338 Repeat .................345 Return ..................345 Send( ...................350 Stop .....................362 Then .....................366 While ....................369

randInt( ................342 randM( .................342 randNorm( ...........342 Scatter .................349 Select( ..................350 SetLEdit ...............351 ShwSt ..................354

SinR .....................357 Sortx ....................359 Sorty ....................359 StReg( ..................362 TwoVar ................368 xyline ...................370

Programming Asm( .................... 269 AsmComp( .......... 270 AsmPrgm ............ 270 CILCD .................. 273 DelVar( ................ 280 Disp ..................... 283 DispG .................. 283

DispT ................... 284 DS<( .................... 288 Else ..................... 290 End ...................... 290 Equal: = ............... 290 Equal to: == ......... 291 For( ...................... 297

Get( ..................... 299 getKy................... 300 Goto .................... 300 IAsk ..................... 304 IAuto ................... 304 If .......................... 305 InpSt.................... 307

Statistics Box ...................... 272 ExpR .................... 293 fcstx..................... 294 fcsty..................... 294 Hist ...................... 303 LgstR ................... 313 LinR ..................... 315

LnR ...................... 317 MBox ................... 319 OneVar ................ 327 P2Reg.................. 330 P3Reg.................. 331 P4Reg.................. 332 PlOff .................... 334

PlOn .................... 334 Plot1(................... 335 Plot2(................... 335 Plot3(................... 335 PwrR ................... 339 rand ..................... 341 randBin( .............. 341

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Strings Concatenation: + .. 274 Eq4St( .................. 290

lngth .................... 316

St4Eq( .................. 361

String entry: " .......363

sub( ......................363

4Sph .....................360 SphereV ...............360 unitV ....................368 vc4li ......................369

Vector entry: [ ] ....369

Vectors cnorm .................. 273 cross( .................. 277 4Cyl ...................... 278 CylV ..................... 278

dim ...................... 281 ¶dim .................... 281 dot( ...................... 285 Fill( ...................... 295

li4vc ..................... 316 norm.................... 323 RectV .................. 344 rnorm .................. 346

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Alphabetical Listing of Operations All the operations in this section are included in the CATALOG. Non-alphabetic operations (such as +, !, and >) are listed at the end of the CATALOG. In this A to Z Reference, however, these operations are listed under their alphabetic equivalent (such as addition, factorial, and greater than). You always can use the CATALOG to select an operation and paste it to the home screen or to a command line in the program editor. You also can use the specific keystrokes, menus, or screens listed in this section. † Indicates menus or screens that paste the operation’s name only if you are in the program editor. In most cases, you can use these menus or screens from the home screen to perform the operation interactively, without pasting the name. ‡ Indicates menus or screens that are valid only from the program editor’s main menu. From the home screen, you cannot use these menus or screens to select an operation.

program editor’s main menu

The syntax for some operations uses brackets [ ] to indicate optional arguments. If you use an optional argument, do not enter the brackets.

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Chapter 20: A to Z Function and Instruction Reference

abs MATH NUM menu CPLX menu MATRX CPLX menu VECTR CPLX menu

abs realNumber or abs (realExpression)

Returns the absolute value of realNumber or realExpression. abs (complexNumber)

Returns the magnitude (modulus) of complexNumber.

abs L256.4 b

267 256.4

abs L4…3+13 b abs (L4…3+13) b

25 1

abs (3,4) b abs (3±4) b

5 3

abs (real,imaginary) returns (real 2+imaginary2). abs (magnitude±angle) returns magnitude. abs list abs matrix abs vector

abs {1.25,L5.67} b {1.25 5.67} abs [(3,4),(3±4)] b [5 3]

Returns a list, matrix, or vector in which each element is the absolute value of the corresponding real or complex element in the argument.

Addition: + \

numberA + numberB Returns the sum of two real or complex numbers. number + list Returns a list in which a real or complex number is added to each element of a real or complex list.

In RectC complex number mode: (2,5)+(5,9) b 4+{1,2,3} b

(7,14) {5 6 7}

3+{1,7,(2,1)} b {(4,0) (10,0) (5,1)}

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Chapter 20: A to Z Function and Instruction Reference listA + listB matrixA + matrixB vectorA + vectorB Returns a list, matrix, or vector that is the sum of the corresponding real or complex elements in the arguments. The two arguments must have the same dimension.

{1,2,3}+{4,5,6} b

{5 7 9}

[[1,2,3][4,5,6]]+[[4,5,6][7,8,9]] [[5 7 9 ] b [11 13 15]] [1,2,3]+[4,5,6] b

[5 7 9]

For information about adding two strings, refer to Concatenation on page 274.

and BASE BOOL menu

integerA and integerB Compares two real integers bit by bit. Internally, both integers are converted to binary. When corresponding bits are compared, the result is 1 if both bits are 1; otherwise, the result is 0. The returned value is the sum of the bit results. For example, 78 and 23 = 6.

In Dec number base mode: 78 and 23 b

6

In Bin number base mode: 1001110 and 10111 b Ans4Dec b

78 = 1001110Ü 23 = 0010111Ü 0000110Ü = 6 You can enter real numbers instead of integers, but they are truncated automatically before the comparison.

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Chapter 20: A to Z Function and Instruction Reference

angle

angle (complexNumber)

Returns the polar angle of complexNumber, adjusted by +p in the 2nd quadrant or Lp in the 3rd quadrant. The polar angle of a real number is always 0.

CPLX menu MATRX CPLX menu VECTR CPLX menu

L1

angle (real,imaginary) returns tan (imaginary/real). angle (magnitude±angle) returns angle, Lp < angle  p. angle complexList angle complexMatrix angle complexVector

269

In Radian angle mode and PolarC complex number mode: angle (3,4) b

.927295218002

angle (3±2) b

2

(6±p/3)¶A b angle A b

(6±1.0471975512) 1.0471975512

angle {(3,4),(3±2)} b {.927295218002 2}

Returns a list, matrix, or vector in which each element is the polar angle of the corresponding element in the argument. If complexVector has only two real elements, the returned value is a real number, not a vector.

Ans -¡

arc( CALC menu

Asm( CATALOG

Ans

Returns the last answer. arc (expression,variable,start,end)

Returns the length along expression with respect to variable, from variable = start to variable = end.

1.7¹4.2 b 147/Ans b

7.14 20.5882352941

arc(x 2,x,0,1) b 1.47894285752 arc(cos x,x,0,p) b 3.82019778904

Asm(assemblyProgramName)

Executes an assembly language program. For more information, refer to Chapter 16.

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AsmComp( CATALOG

AsmComp(AsciiAssemblyPrgmName,HexAssemblyPrgmName)

Compiles an assembly language program written in ASCII and stores the hex version. The compiled hex version, which uses about half the storage space of the ASCII version, cannot be edited. When you execute the ASCII version, the TI-86 compiles it each time. To speed up execution, use AsmComp( to compile the ASCII version once and then execute the hex version each time you want to run the program.

AsmPrgm CATALOG

Assignment: = 1 ã= ä

aug( LIST OPS menu MATRX OPS menu

AsmPrgm

Must be used as the first line of an assembly language program. equationVariable = expression Stores expression to equationVariable, without evaluating expression. (If you use X to store an expression to a variable, the expression is evaluated and then the result is stored.) aug(listA,listB)

Returns a list consisting of listB appended (concatenated) to the end of listA. The lists can be real or complex.

y1=2 x 2+6 xN5 b

Done

The built-in equation variables used for graphing are case-sensitive. Use y1, not Y1.

aug({1,L3,2},{5,4}) b {1 L3 2 5 4}

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Chapter 20: A to Z Function and Instruction Reference aug(matrixA,matrixB)

Returns a matrix consisting of matrixB appended as new columns to the end of matrixA. The matrices can be real or complex. Both must have the same number of rows. aug(matrix,vector)

Returns a matrix consisting of vector appended as a new column to the end of matrix. The arguments can be real or complex. The number of rows in matrix must equal the number of elements in vector.

Axes( † GRAPH VARS menu

AxesOff † graph format screen

AxesOn † graph format screen

Ü

Axes(xAxisVariable,yAxisVariable)

[[1,2,3][4,5,6]]¶MATA b [[1 2 3] [4 5 6]] [[7,8][9,10]]¶MATB b [[7 8 ] [9 10]] aug(MATA,MATB) b [[1 2 3 7 8 ] [4 5 6 9 10]]

Axes(Q1,Q2) b

Done

Specifies the variables plotted for the axes in DifEq graphing mode. The xAxisVariable or yAxisVariable can be t, Q1 through Q9, or Q¢1 through Q¢9. AxesOff

Turns off the graph axes. AxesOn

Turns on the graph axes. integer Ü

BASE TYPE menu

271

Designates a real integer as binary, regardless of the number base mode setting.

In Dec number base mode: 10Ü b 10Ü+10 b

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Chapter 20: A to Z Function and Instruction Reference

Bin

Bin

4Bin BASE CONV menu

In Bin number base mode:

Sets binary number base mode. Results are displayed with the Ü suffix. In any number base mode, you can designate an appropriate value as binary, decimal, hexadecimal, or octal by using the Ü, Þ, ß, or Ý designator, respectively, from the BASE TYPE menu.

† mode screen

number 4Bin list 4Bin matrix 4Bin vector 4Bin Returns the binary equivalent of the real or complex argument.

Box

Box xList,frequencyList

Draws a box plot on the current graph, using the real data in xList and the frequencies in frequencyList.

† STAT DRAW menu

Box xList

Uses frequencies of 1.

10+Úß+10Ý+10Þ b

100011Ü

In Dec number base mode: 2¹8 b Ans4Bin b

16 10000Ü

{1,2,3,4}4Bin b {1Ü 10Ü 11Ü 100Ü}

Starting with a ZStd graph screen: {1,2,3,4,5,9}¶XL b {1 2 3 4 5 9} {1,1,1,4,1,1}¶FL b {1 1 1 4 1 1} 0¶xMin:0¶yMin b 0 Box XL,FL b

Box

Uses the data in built-in variables xStat and fStat. These variables must contain valid data of the same dimension; otherwise, an error occurs.

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Chapter 20: A to Z Function and Instruction Reference

Circl(

Circl(x,y,radius)

Draws a circle with center (x,y) and radius on the current graph.

† GRAPH DRAW menu

ClDrw

273

Starting with a ZStd graph screen: ZSqr:Circl(1,2,7) b

ClDrw

Clears all drawn elements from the current graph.

† GRAPH DRAW menu † STAT DRAW menu

CILCD

ClLCD

Clears the home screen (LCD).

‡ program editor I/O menu

ClrEnt

ClrEnt

Clears the contents of the Last Entry storage area.

MEM menu

ClTbl ‡ program editor I/O menu

cnorm MATRX MATH menu

ClTbl

Clears all values from the current table if Indpnt: Ask (IAsk, page 304) is set. cnorm matrix

Returns the column norm of a real or complex matrix. For each column, cnorm sums the absolute values (magnitudes of complex elements) of the elements in that column and returns the largest of those column sums.

[[1,L2,3][4,5,L6]]¶MAT b [[1 L2 3 ] [4 5 L6]] cnorm MAT b 9

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Chapter 20: A to Z Function and Instruction Reference cnorm vector

Returns the sum of the absolute values of the real or complex elements in vector.

Concatenation: + \

cond MATRX MATH menu

stringA + stringB Returns a string consisting of stringB appended (concatenated) to the end of stringA. cond squareMatrix

Returns the condition number of a real or complex squareMatrix, which is calculated as: cnorm squareMatrix ¹ cnorm squareMatrixL1

The condition number indicates how well-behaved squareMatrix is expected to be for certain matrix functions, particularly inverse. For a well-behaved matrix, the condition number is close to 1. log(cond squareMatrix) indicates the number of digits

that may be lost due to round-off errors in computing the inverse.

[L1,2,L3]¶VEC b cnorm VEC b

[L1 2 L3] 6

"your name:"¶STR b your name: "Enter "+STR b Enter your name: [[1,0,0][0,1,0][0,0,1]]¶MAT1 [[1 0 0] b [0 1 0] [0 0 1]] cond MAT1 b log (Ans) b

1 0

[[1,2,3][4,5,6][7,8,9]]¶MAT2 [[1 2 3] b [4 5 6] [7 8 9]] cond MAT2 b log (Ans) b

For a matrix with no inverse, cond returns an error.

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Chapter 20: A to Z Function and Instruction Reference

conj

conj (complexNumber)

CPLX menu

Returns the complex conjugate of complexNumber.

MATRX CPLX menu

In RectC mode, conj (real,imaginary) returns (real,Limaginary).

VECTR CPLX menu

In PolarC mode, conj (magnitude±angle) returns (magnitude±Langle), Lp < angle  p. conj complexList conj complexMatrix conj complexVector

In RectC complex number mode: conj (3,4) b (3,L4) conj (3±2) b (L1.24844050964,L2.7… In PolarC complex number mode: conj (3±2) b conj (3,4) b

† graph format screen

CoordOn † graph format screen

(3±L2)

(5±L.927295218002) conj {‡L2,(3,4)} b {(1.41421356237±L1.5…

Returns a complex list, matrix, or vector in which each element is the complex conjugate of the original.

CoordOff

275

CoordOff

Turns off cursor coordinates so they are not displayed at the bottom of a graph. CoordOn

Displays cursor coordinates at the bottom of a graph.

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cos

cos angle or cos (expression)

>

cos p/2 b cos (p/2) b cos 45¡ b

An angle is interpreted as degrees or radians according to the current angle mode. In any angle mode, you can designate an angle as degrees or radians by using the ¡ or r designator, respectively, from the MATH ANGLE menu.

cos 45 b cos (p/2) r b

cos list

Returns a list in which each element is the cosine of the corresponding element in list. cos squareMatrix The squareMatrix cannot have repeated eigenvalues.

cos L1 -|

In Radian angle mode:

Returns the cosine of angle or expression, which can be real or complex.

L.5 0 .707106781187

In Degree angle mode: .707106781187 0

In Radian angle mode: cos {0,p/2,p} b

{1 0 L1}

In Degree angle mode: cos {0,60,90} b

{1 .5 0}

Returns a square matrix that is the matrix cosine of squareMatrix. The matrix cosine corresponds to the result calculated using power series or Cayley-Hamilton Theorem techniques. This is not the same as simply calculating the cosine of each element. cos L1 number or cosL1 (expression)

Returns the arccosine of number or expression, which can be real or complex.

In Radian angle mode: cosL1 .5 b In Degree angle mode: cosL1 1 b

cos L1 list

Returns a list in which each element is the arccosine of the corresponding element in list.

1.0471975512 0

In Radian angle mode: cos L1 {0,.5} b {1.57079632679,1.047…

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Chapter 20: A to Z Function and Instruction Reference

cosh MATH HYP menu

cosh number or cosh (expression)

Returns a list in which each element is the hyperbolic cosine of the corresponding element in list.

MATH HYP menu

cosh L1 number or cosL1 (expression)

Returns a list in which each element is the inverse hyperbolic cosine of the corresponding element in list.

VECTR MATH menu

cosh {0,1.2} b {1 1.81065556732}

coshL1 1 b

0

Returns the inverse hyperbolic cosine of number or expression, which can be real or complex. cosh L1 list

cross(

1.81065556732

Returns the hyperbolic cosine of number or expression, which can be real or complex. cosh list

cosh L1

cosh 1.2 b

277

cross(vectorA,vectorB)

Returns the cross product of two real or complex vectors, where:

coshL1 {1,2.1,3} b {0 1.37285914424 1.7…

cross([1,2,3],[4,5,6]) b [L3 6 L3] cross([1,2],[3,4]) b

cross([a,b,c],[d,e,f]) = [bfNce cdNaf aeNbd]

Both vectors must have the same dimension (either 2 or 3 elements). A 2-D vector is treated as a 3-D vector with 0 as the third element.

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[0 0 L2]

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Chapter 20: A to Z Function and Instruction Reference

cSum(

cSum(list)

Returns a list of the cumulative sums of the real or complex elements in list, starting with the first element.

LIST OPS menu

4Cyl

vector 4Cyl Displays a 2- or 3-element real vector result in cylindrical form, [rq z], even if the display mode is not set for cylindrical (CylV).

VECTR OPS menu

CylV

CylV

Sets cylindrical vector coordinate mode ( [rq z] ).

† mode screen

Þ

number Þ Designates a real number as decimal, regardless of the number base mode setting.

BASE TYPE menu

Dec † mode screen

Dec

cSum({1,2,3,4}) b

{1 3 6 10}

{10,20,30}¶L1 b cSum(L1) b

{10 20 30} {10 30 60}

[L2,0]4Cyl b [23.14159265359 0] [L2,0,1]4Cyl b [23.14159265359 1] In CylV vector coordinate mode and Radian angle mode: [3,4,5] b

[5.927295218002 5]

In Bin number base mode: 10Þ b 10Þ+10 b

1010Ü 1100Ü

In Dec number base mode:

Sets decimal number base mode. In any number base mode, you can designate an appropriate value as binary, decimal, hexadecimal, or octal by using the Ü, Þ, ß, or Ý designator, respectively, from the BASE TYPE menu.

10+10Ü+Úß+10Ý b

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Chapter 20: A to Z Function and Instruction Reference

4Dec BASE CONV menu

number 4Dec list 4Dec matrix 4Dec vector 4Dec Returns the decimal equivalent of the real or complex argument.

Degree

Degree

Sets degree angle mode.

† mode screen

Degree entry: ¡

number ¡ or (expression) ¡ Designates a real number or expression as degrees, regardless of the angle mode setting.

MATH ANGLE menu

list ¡ Designates each element in list as degrees.

Deltalst( LIST OPS menu (Deltal shows on menu)

Deltalst(list)

Returns a list containing the differences between consecutive real or complex elements in list. This subtracts the first element in list from the second element, the second from the third, and so on. The resulting list is always one element shorter than list.

279

In Hex number base mode: 2¹Ú b Ans4Dec b

1Ùß 30Þ

{Õ,Ö,×,Ø,Ù}4Dec b {10Þ 11Þ 12Þ 13Þ 14Þ}

In Degree angle mode: sin 90 b sin (p/2) b

1 .027412133592

In Radian angle mode: cos 90 b cos 90¡ b

L.448073616129 0

cos {45,90,180}¡ b {.707106781187 0 L1} Deltalst({20,30,45,70}) b {10 15 25}

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DelVar( ‡ program editor CTL menu (DelVa shows on menu)

der1( CALC menu

DelVar(variable)

Deletes the specified user-created variable from memory.

2¶A b 2 16 (A+2) 2 b DelVar(A) b Done ERROR 14 UNDEFINED (A+2) 2 b

You cannot use DelVar( to delete a program variable or built-in variable. der1(expression,variable,value)

der1(x^3,x,5) b

75

3¶x b der1(x^3,x) b

3 27

Returns the first derivative of expression with respect to variable at the real or complex value. der1(expression,variable)

Uses the current value of variable. der1(expression,variable,list)

der1(x^3,x,{5,3}) b

{75 27}

Returns a list containing the first derivatives at the values specified by the elements in list.

der2( CALC menu

der2(expression,variable,value)

der2(x^3,x,5) b

30

3¶x b der2(x^3,x) b

3 18

Returns the second derivative of expression with respect to variable at the real or complex value. der2(expression,variable)

Uses the current value of variable. der2(expression,variable,list)

der2(x^3,x,{5,3}) b

Returns a list containing the second derivatives at the values specified by the elements in list.

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Chapter 20: A to Z Function and Instruction Reference

det

det squareMatrix

Returns the determinant of squareMatrix. The result is real for a real matrix, complex for a complex matrix.

MATRX MATH menu

DifEq † mode screen

dim MATRX OPS menu VECTR OPS menu

[[1,2][3,4]]¶MAT b det MAT b

281 [[1 2] [3 4]] L2

DifEq

Sets differential equation graphing mode. dim matrix

Returns a list containing the dimensions (number of rows and columns) of a real or complex matrix. dim vector

[[2,7,1][L8,0,1]]¶MAT b [[2 7 1] [L8 0 1]] dim MAT b {2 3} dim [L8,0,1] b

3

Returns the length (number of elements) of a real or complex vector.

¶dim

{rows,columns}¶dim matrixName

X, then MATRX OPS menu

If matrixName does not exist, creates a new matrix with the specified dimensions and fills it with zeros.

X, then VECTR OPS menu

If matrixName exists, redimensions that matrix to the specified dimensions. Existing elements within the new dimensions are not changed; elements outside the new dimensions are deleted. If additional elements are created, they are filled with zeros.

[[2,7][L8,0]]¶MAT b [[2 7] [L8 0]] {3,3}¶dim MAT b MAT b

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{3 3} [[2 7 0] [L8 0 0] [0 0 0]]

282

Chapter 20: A to Z Function and Instruction Reference #ofElements¶dim vectorName If vectorName does not exist, creates a new vector with the specified #ofElements and fills it with zeros. If vectorName exists, redimensions that vector to the specified #ofElements. Existing elements within the new dimension are not changed; elements outside the new dimension are deleted. If additional elements are created, they are filled with zeros.

dimL LIST OPS menu

¶dimL X, then LIST OPS menu

dimL list

Returns the length (number of elements) of a real or complex list. #ofElements¶dimL listName If listName does not exist, creates a new list with the specified #ofElements and fills it with zeros. If listName exists, redimensions that list to the specified #ofElements. Existing elements within the new dimension are not changed; elements outside the new dimension are deleted. If additional elements are created, they are filled with zeros.

DirFld † graph format screen (scroll down to second screen)

DelVar(VEC) b 4¶dim VEC b VEC b

Done 4 [0 0 0 0]

[1,2,3,4]¶VEC b 2¶dim VEC b VEC b 3¶dim VEC b VEC b

[1 2 3 4] 2 [1 2] 3 [1 2 0]

dimL {2,7,L8,0} b 1/dimL {2,7,L8,0} b

3¶dimL NEWLIST b NEWLIST b {2,7,L8,1}¶L1 b 5¶dimL L1 b L1 b 2¶dimL L1 b L1 b

DirFld

In DifEq graphing mode, turns on direction fields. To turn off direction and slope fields, use FldOff.

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4 .25

3 {0 0 0} {2 7 L8 1} 5 {2 7 L8 1 0} 2 {2 7}

Chapter 20: A to Z Function and Instruction Reference

Disp

Disp valueA,valueB,valueC, ...

Displays each value. The values can include strings and variable names.

‡ program editor I/O menu

Displays the home screen.

† GRAPH menu ‡ program editor I/O menu

10 1024 Done

"Hello"¶STR b Hello Disp STR+", Jan" b Hello, Jan Done

Disp

DispG

10¶x b Disp x^3+3 xN6 b

283

DispG

Program segment in Func graphing mode:

Displays the current graph.

Function names are case-sensitive. Use y1, not Y1.

To select from a list of window variable names, press w / / *.

© :y1=4cos x :L10¶xMin:10¶xMax :L5¶yMin:5¶yMax :DispG ©

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DispT ‡ program editor I/O menu

Division: / F

DispT

Program segment in Func graphing mode:

Displays the table. Function names are case-sensitive. Use y1, not Y1.

numberA / numberB or (expressionA) / (expressionB) Returns one argument divided by another. The arguments can be real or complex. number / list or (expression) / list

© :y1=4cos x :DispT ©

L98/4 b L98/(4¹3) b

L24.5 L8.16666666667

100/{10,25,2} b

{10 4 50}

{120,92,8}/4 b

{30 23 2}

Returns a list in which each element is number or expression divided by the corresponding element in list. list / number or list / (expression) vector / number or vector / (expression) Returns a list or vector in which each element of list or vector is divided by number or expression. listA / listB

In RectC complex number mode: [8,1,(5,2)]/2 b [(4,0) (.5,0) (2.5,1… {1,2,3}/{4,5,6} b

Returns a list in which each element of listA is divided by the corresponding element of listB. The lists must have the same dimension.

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{.25 .4 .5}

Chapter 20: A to Z Function and Instruction Reference

DMS entry: ' MATH ANGLE menu In a trig calculation, the result of a DMS entry is treated as degrees in the Degree angle mode only. It is treated as radians in Radian angle mode.

4DMS MATH ANGLE menu

dot( VECTR MATH menu

degrees'minutes'seconds' Designates the entered angle is in DMS format. degrees ( 999,999), minutes (< 60), and seconds (< 60, may have decimal places) must be entered as real numbers, not as variable names or expressions. Do not use ¡ and " symbols to specify degrees and seconds. For example, 5¡59' is interpreted as implied multiplication of 5¡ ¹ 59' according to the current angle mode setting. angle 4DMS Displays angle in DMS format. The result is shown in degrees¡minutes'seconds" format, even though you use degrees'minutes'seconds' to enter a DMS angle. dot(vectorA,vectorB)

54'32'30' b

† graph format screen

54.5416666667

In Degree angle mode: cos 54'32'30' b

.580110760699

In Radian angle mode: cos 54'32'30' b

L.422502666138

Do not use the following notation; in Degree angle mode: 5¡59' b

295

In Degree angle mode: 45.3714DMS b 54'32'30'¹2 b Ans4DMS b

45¡22'15.6" 109.083333333 109¡5'0"

dot([1,2,3],[4,5,6]) b

Returns the dot product of two real or complex vectors. dot([a,b,c],[d,e,f]) returns a¹d+b¹e+c¹f.

DrawDot

285

DrawDot

Sets dot graphing format.

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Chapter 20: A to Z Function and Instruction Reference

DrawF GRAPH DRAW menu

DrawLine † graph format screen

DrawF expression

Draws expression (in terms of x) on the current graph.

In Func graphing mode: ZStd:DrawF 1.25 x cos x b

DrawLine

Sets connected line graphing format.

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Chapter 20: A to Z Function and Instruction Reference

DrEqu( † GRAPH menu To enter the ' character for the Q' variables, use the CHAR MISC menu.

DrEqu(xAxisVariable,yAxisVariable,xList,yList,tList)

In DifEq graphing mode, draws the solution to a set of differential equations stored in the Q' variables specified by xAxisVariable and yAxisVariable. If direction fields are off (FldOff is selected), the initial values must be stored also.

287

In DifEq graphing mode, starting with a ZStd graph screen: Q'1=Q2:Q'2=LQ1 b 0¶tMin:1¶QI1:0¶QI2 b DrEqu(Q1,Q2,XL,YL,TL) b

After the solution is drawn, DrEqu( waits for you to move the cursor to a new initial value and press b to draw the new solution. You then are prompted to press Y (to specify another initial value) or N (to stop).

Move the cursor to a new initial value. b

For the last-drawn solution, the x, y, and t values (beginning at their initial values) are stored to xList, yList, and tList, respectively. DrEqu(xAxisVariable,yAxisVariable)

Does not store x, y, and t values for the solution.

DrInv GRAPH DRAW menu

DrInv expression

Draws the inverse of expression by plotting x values on the y-axis and y values on the x-axis.

Press N to stop graphing. You can then examine XL, YL, and TL. In Func graphing mode: ZStd:DrInv 1.25 x cos x b

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DS<( ‡ program editor CTL menu

:DS<(variable,value) :command-if-variable‚value :commands

Decrements variable by 1. If the result is < value, skips command-if-variable‚value. If the result is ‚ value, then command-if-variable‚value is executed.

Program segment: © :9¶A :Lbl Start :Disp A :DS<(A,5) :Goto Start :Disp "A is now <5" ©

variable cannot be a built-in variable.

dxDer1 † mode screen

dxNDer † mode screen

e^ -‚

dxDer1

Sets der1 as the current differentiation type. der1 differentiates exactly and calculates the value for each function in an expression. It is more accurate than dxNDer, but more restrictive in that only certain functions are valid in the expression. dxNDer

Sets nDer as the current differentiation type. nDer differentiates numerically and calculates the value for an expression. It is less accurate than dxDer1, but less restrictive in the functions that are valid in the expression. e^power or e^(expression)

The current differentiation type is used by the arc( and TanLn( functions, as well as interactive graphing operations dy/dx, dr/dq, dy/dt, dx/dt, ARC, TanLn, and INFLC.

The current differentiation type is used by the arc( and TanLn( functions, as well as interactive graphing operations dy/dx, dr/dq, dy/dt, dx/dt, ARC, TanLn, and INFLC.

e^0 b

Returns e raised to power or expression. The argument can be real or complex.

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Chapter 20: A to Z Function and Instruction Reference e^list

Returns a list in which each element is e raised to the power specified by the corresponding element in list.

289

e^{1,0,.5} b {2.71828182846 1 1.6…

e^squareMatrix The squareMatrix cannot have repeated eigenvalues.

eigVc MATRX MATH menu The squareMatrix cannot have repeated eigenvalues.

eigVl MATRX MATH menu

Returns a square matrix that is the matrix exponential of squareMatrix. The matrix exponential corresponds to the result calculated using power series or CayleyHamilton Theorem techniques. This is not the same as simply calculating the exponential of each element. eigVc squareMatrix

Returns a matrix containing the eigenvectors for a real or complex squareMatrix, where each column in the result corresponds to an eigenvalue. The eigenvectors of a real matrix may be complex. Note that an eigenvector is not unique; it may be scaled by any constant factor. TI-86 eigenvectors are normalized. eigVl squareMatrix

Returns a list of the eigenvalues of a real or complex squareMatrix. The eigenvalues of a real matrix may be complex.

In RectC complex number mode: [[L1,2,5][3,L6,9][2,L5,7]]¶MAT [[L1 2 5] b [3 L6 9] [2 L5 7]] eigVc MAT b [[(.800906446592,0) … [(L.484028886343,0)… [(L.352512270699,0)… In RectC complex number mode: [[L1,2,5][3,L6,9][2,L5,7]]¶MAT [[L1 2 5] b [3 L6 9] [2 L5 7]] eigVl MAT b {(L4.40941084667,0) …

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Chapter 20: A to Z Function and Instruction Reference

Else ‡ program editor CTL menu

End

Refer to syntax information for If, beginning on page 305. See the If:Then:Else:End syntax. End

Identifies the end of a While, For, Repeat, or If-Then-

‡ program editor CTL menu

Eng † mode screen

Else loop. Eng

In Eng notation mode:

Sets engineering notation mode, in which the power-of10 exponent is a multiple of 3.

123456789 b 123456789 b

Eq4St( STRNG menu

Eq4St(equationVariable,stringVariable)

Converts the contents of equationVariable to a string and stores it to stringVariable. Be sure to specify an equation variable, not an equation. To create an equation variable, use an equal sign (=) to define the variable. For example, enter A=B¹C, not B¹C¶A.

Equal: = 1 ã= ä

Refer to syntax information for Assignment on page 270. If you use = in an expression in which the first argument is not a variable name at the beginning of a line, the = is treated as N(.

123.456789E6

In Normal notation mode: A=B¹C b 5¶B b 2¶C b A b Eq4St(A,STR) b STR b

123456789 Done 5 2 10 Done B¹C

Example of = treated as N(, where 4=6+1 is evaluated as 4N(6+1): 4=6+1 b

L3

For true/false comparison, use == instead: 4==6+1 b

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Chapter 20: A to Z Function and Instruction Reference

Equal to: == TEST menu The == operator is used to compare arguments, while = is used to assign a value or expression to a variable.

numberA == numberB matrixA == matrixB vectorA == vectorB stringA == stringB Tests whether the condition argumentA == argumentB is true or false. Numbers, matrices, and vectors can be real or complex. If complex, the magnitude (modulus) of each element is compared. Strings are case-sensitive.

291

2+2==2+2 b

1

2+(2==2)+2 b

5

[1,2]==[3N2,L1+3] b

1

"A"=="a" b

0

• If true (argumentA = argumentB), returns 1. • If false (argumentA ƒ argumentB), returns 0. listA == listB

{1,5,9}=={1,L6,9} b

{1 0 1}

Returns a list of 1s and/or 0s to indicate if each element in listA is = the corresponding element in listB.

Euler † graph format screen (scroll down to second screen)

eval MATH MISC menu

Euler

In DifEq graphing mode, uses an algorithm based on the Euler method to solve differential equations. Typically, Euler is less accurate than RK but finds the solutions much quicker. eval xValue

Returns a list containing the y values of all defined and selected functions evaluated at a real xValue.

Remember that built-in equation variables y1 and y2 are case-sensitive: y1=x^3+x+5 b y2=2 x b eval 5 b

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evalF( CALC menu

evalF(expression,variable,value)

evalF(expression,variable,list)

Returns a list containing the values of expression evaluated with respect to variable at each element in list.

Exponent: E C

evalF(x^3+x+5,x,5) b

135

Returns the value of expression evaluated with respect to variable at a real or complex value.

number E power or (expressionA) E (expressionB) Returns a real or complex number raised to the power of 10, where power is a real integer such that L999 < power < 999. Any expressions must evaluate to appropriate values. list E power or list E (expression)

evalF(x^3+x+5,x,{3,5}) b {35 135}

12.3456789E5 b (1.78/2.34)E2 b

1234567.89 76.0683760684

{6.34,854.6}E3 b

Returns a list in which each element is the corresponding element in list raised to the power of 10.

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Chapter 20: A to Z Function and Instruction Reference

ExpR STAT CALC menu

Built-in equation variables such as y1, r1, and xt1 are case-sensitive. Do not use Y1, R1, and XT1.

ExpR xList,yList,frequencyList,equationVariable

Fits an exponential regression model (y=ab x) to real data pairs in xList and yList (y values must be > 0) and frequencies in frequencyList. The regression equation is stored to equationVariable, which must be a built-in equation variable such as y1, r1, and xt1.

293

In Func graphing mode: {1,2,3,4,5}¶L1 b {1 2 3 4 5} {1,20,55,230,742}¶L2 b {1 20 55 230 742} ExpR L1,L2,y1 b

Values used for xList, yList, and frequencyList are stored automatically to built-in variables xStat, yStat, and fStat, respectively. The regression equation is stored also to built-in equation variable RegEq. ExpR xList,yList,equationVariable

Uses frequencies of 1.

Plot1(1,L1,L2) b ZData b

ExpR xList,yList,frequencyList

Stores the regression equation to RegEq only. ExpR xList,yList

Uses frequencies of 1, and stores the regression equation to RegEq only. ExpR equationVariable

Uses xStat, yStat, and fStat for xList, yList, and frequencyList, respectively. These built-in variables must contain valid data of the same dimension; otherwise, an error occurs. The regression equation is stored to equationVariable and RegEq.

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Chapter 20: A to Z Function and Instruction Reference ExpR

Uses xStat, yStat, and fStat, and stores the regression equation to RegEq only.

Factorial: !

number ! or (expression) ! Returns the factorial of a real integer or non-integer, where 0  integer  449 and 0  non-integer  449.9. For a non-integer, the Gamma function is used to find the factorial. An expression must evaluate to an appropriate value.

MATH PROB menu

6! b 12.5! b

{6,7,8}! b

list ! Returns a list in which each element is the factorial of the corresponding element in list.

fcstx † STAT menu

fcsty † STAT menu

fcstx yValue

Based on the current regression equation (ReqEq), returns the forecasted x at a real yValue. fcsty xValue

Based on the current regression equation (ReqEq), returns the forecasted y at a real xValue.

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Chapter 20: A to Z Function and Instruction Reference

Fill( LIST OPS menu MATRX OPS menu

Fill(number,listName) Fill(number,matrixName) Fill(number,vectorName)

Replaces each element in an existing listName, matrixName, or vectorName with a real or complex number.

VECTR OPS menu

Fix

Fix integer or Fix (expression)

Sets fixed decimal mode for integer number of decimal places, where 0  integer  11. An expression must evaluate to an appropriate integer.

† mode screen

FldOff

† mode screen

{3 4 5} Done {8 8 8}

Fill((3,4),L1) b Done L1 b {(3,4) (3,4) (3,4)}

Fix 3 b p/2 b Float b p/2 b

Done 1.571 Done 1.57079632679

FldOff

In DifEq graphing mode, turns off the slope and direction fields. To turn on slope fields, use SlpFld. To turn on direction fields, use DirFld.

† graph format screen (scroll down to second screen)

Float

{3,4,5}¶L1 b Fill(8,L1) b L1 b

295

Float

In Radian angle mode:

Sets floating decimal mode.

Fix 11 b sin (p/6) b Float b sin (p/6) b

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Chapter 20: A to Z Function and Instruction Reference

fMax( CALC menu

fMax(expression,variable,lower,upper)

Returns the value at which a local maximum of expression with respect to variable occurs, between real lower and upper values for variable.

fMax(sin x,x,Lp,p) b 1.57079632598

The tolerance is controlled by the built-in variable tol, whose default is 1EL5. To view or set tol, press - ™ ) to display the tolerance editor.

fMin( CALC menu

fMin(expression,variable,lower,upper)

Returns the value at which a local minimum of expression with respect to variable occurs, between real lower and upper bounds for variable.

fMin(sin x,x,Lp,p) b L1.57079632691

The tolerance is controlled by the built-in variable tol, whose default is 1EL5. To view or set tol, press - ™ ) to display the tolerance editor.

fnInt( CALC menu

fnInt(expression,variable,lower,upper)

fnInt(x 2,x,0,1) b .333333333333

Returns the numerical function integral of expression with respect to variable, between real lower and upper bounds for variable. The tolerance is controlled by the built-in variable tol, whose default is 1EL5. To view or set tol, press - ™ ) to display the tolerance editor.

FnOff † GRAPH VARS menu

FnOff function#,function#, ...

FnOff 1,3 b

Deselects the specified equation function numbers.

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Chapter 20: A to Z Function and Instruction Reference FnOff

297

FnOff b

Done

FnOn 1,3 b

Done

FnOn b

Done

Deselects all equation function numbers.

FnOn

FnOn function#,function#, ...

Selects the specified equation function numbers, in addition to any others already selected.

† GRAPH VARS menu

FnOn

Selects all equation function numbers.

For( ‡ program editor CTL menu

:For(variable,begin,end,step) or :loop :End :commands

:For(variable,begin,end) :loop :End :commands

Executes the commands in loop iteratively, where the number of repetitions is controlled by variable. The first time through the loop, variable = begin. At the End of the loop, variable is incremented by step. The loop is repeated until variable > end. If you do not specify step, the default is 1. You can specify values such that begin > end. If so, be sure to specify a negative step.

Program segment: © For(A,0,8,2) Disp A 2 End © Displays 0, 4, 16, 36, and 64.

© For(A,0,8) Disp A 2 End © Displays 0, 1, 4, 9, 16, 25, 36, 49, and 64.

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Form( LIST OPS menu

Form("formula",listName)

Generates the contents of listName automatically, based on the attached formula. If you express formula in terms of a list, you can generate one list based on the contents of another. The contents of listName are updated automatically if you edit formula or edit a list referenced in formula.

fPart MATH NUM menu

fPart number or fPart (expression)

Returns the fractional part of a real or complex number or expression. fPart list fPart matrix fPart vector

Returns a list, matrix, or vector in which each element is the fractional part of the corresponding element in the specified argument.

4Frac MATH MISC menu

number 4Frac Displays a real or complex number as its rational equivalent, a fraction reduced to its simplest terms.

{1,2,3,4}¶L1 b {1 2 3 4} Form("10¹L1",L2) b Done L2 b {10 20 30 40} {5,10,15,20}¶L1 b L2 b

{5 10 15 20} {50 100 150 200}

Form("L1/5",L2) b L2 b

Done {1 2 3 4}

fPart 23.45 b

.45

fPart (L17.26¹8) b

L.08

[[1,L23.45][L99.5,47.15]]¶MAT L23.45] [[1 b [L99.5 47.15 ]] fPart MAT b

1/3+2/7 b Ans4Frac b

If number cannot be simplified or if the denominator is more than four digits, the decimal equivalent is returned.

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L.45] [[0 [L.5 .15 ]]

.619047619048 13/21

Chapter 20: A to Z Function and Instruction Reference list 4Frac matrix 4Frac vector 4Frac

299

{1/2+1/3,1/6N3/8}¶L1 b {.833333333333 L.208… Ans4Frac b {5/6 L5/24}

Returns a list, matrix, or vector in which each element is the rational equivalent of the corresponding element in the argument.

Func † mode screen

gcd( MATH MISC menu

Func

Sets function graphing mode. gcd(integerA,integerB)

gcd(listA,listB)

Returns a list in which each element is the gcd of the two corresponding elements in listA and listB.

Get( ‡ program editor I/O menu

gcd(18,33) b

3

Returns the greatest common divisor of two nonnegative integers. gcd({12,14,16},{9,7,5}) b {3 7 1}

Get(variable)

Gets data from a CBL or CBR System or another TI-86 and stores it to variable.

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Chapter 20: A to Z Function and Instruction Reference

getKy ‡ program editor I/O menu

getKy

Returns the key code for the last key pressed. If no key has been pressed, getKy returns 0. Refer to the TI-86 key code diagram in Chapter 16.

Program: PROGRAM:CODES :Lbl TOP :getKy¶KEY :While KEY==0 : getKy¶KEY :End :Disp KEY :Goto TOP To break the program, press ^ and then *.

Goto ‡ program editor CTL menu

Greater than: > TEST menu

Goto label

Transfers (branches) program control to the label specified by an existing Lbl instruction.

numberA > numberB or (expressionA) > (expressionB) Tests whether the condition is true or false. The arguments must be real numbers. • If true (numberA > numberB), returns 1. • If false (numberA  numberB), returns 0.

Program segment: © :0¶TEMP:1¶J :Lbl TOP :TEMP+J¶TEMP :If J<10 :Then : J+1¶J : Goto TOP :End :Disp TEMP © 2>0 b

1

88>123 b

0

L5>L5 b

0

(20¹5/2)>(18¹2) b

1

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Chapter 20: A to Z Function and Instruction Reference number > list

301

1>{1,L6,10} b

{0 1 0}

{1,5,9}>{1,L6,10} b

{0 1 0}

Returns a list of 1s and/or 0s to indicate if number is > the corresponding element in list. listA > listB Returns a list of 1s and/or 0s to indicate if each element in listA is > the corresponding element in listB.

Greater than or equal to: ‚ TEST menu

numberA ‚ numberB or (expressionA) ‚ (expressionB) Tests whether the condition is true or false. The arguments must be real numbers. • If true (numberA ‚ numberB), returns 1. • If false (numberA < numberB), returns 0. number ‚ list

2‚0 b

1

88‚123 b

0

L5‚L5 b

1

(20¹5/2)‚(18¹2) b

1

1‚{1,L6,10} b

{1 1 0}

{1,5,9}‚{1,L6,10} b

{1 1 0}

Returns a list of 1s and/or 0s to indicate if number is ‚ the corresponding element in list. listA ‚ listB Returns a list of 1s and/or 0s to indicate if each element in listA is ‚ the corresponding element in listB.

GridOff † graph format screen

GridOff

Turns off grid format so that grid points are not displayed.

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GridOn

GridOn

Turns on grid format so that grid points are displayed in rows and columns corresponding to the tick marks on each axis.

† graph format screen

GrStl(

GrStl(function#,graphStyle#)

In Func graphing mode:

Sets the graph style for function#. For graphStyle#, specify an integer from 1 through 7:

CATALOG

1 = » (line) 2 = ¼ (thick) 3 = ¾ (above)

4 = ¿ (below) 5 = À (path) 6 = Á (animate)

y1=x sin x b GrStl(1,4) b ZStd b

Done Done

7 = Â (dot)

Depending on the graphing mode, some graph styles may not be available.

ß

integer ß Designates a real integer as hexadecimal, regardless of the number base mode setting.

BASE TYPE menu

Hex † mode screen

Hex

In Dec number base mode: 10ß b 10ß+10 b

16 26

In Hex number base mode:

Sets hexadecimal number base mode. Results are displayed with the ß suffix. In any number base mode, you can designate an appropriate value as binary, decimal, hexadecimal, or octal by using the Ü, Þ, ß, or Ý designator, respectively, from the BASE TYPE menu.

Ú+10Ü+10Ý+10Þ b

To enter hexadecimal numbers Õ through Ú, use the BASE A-F menu. Do not use 1 to type a letter.

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Chapter 20: A to Z Function and Instruction Reference

4Hex BASE CONV menu

number 4Hex list 4Hex matrix 4Hex vector 4Hex

In Bin number base mode: 1010¹1110 b Ans4Hex b

Hist xList,frequencyList

Draws a histogram on the current graph, using the real data in xList and the frequencies in frequencyList.

† STAT DRAW menu

Hist xList

Uses frequencies of 1.

10001100Ü 8×ß

{100,101,110}4Hex b

Returns the hexadecimal equivalent of the real or complex argument.

Hist

303

{4ß 5ß 6ß}

Starting with a ZStd graph screen: {1,2,3,4,6,7}¶XL b {1 2 3 4 6 7} {1,6,4,2,3,5}¶FL b {1 6 4 2 3 5} 0¶xMin:0¶yMin b 0 Hist XL,FL b

Hist

Uses the data in built-in variables xStat and fStat. These variables must contain valid data of the same dimension; otherwise, an error occurs. {1,1,2,2,2,3,3,3,3,3,3,4,4,5,5,5, 7,7}¶XL b {1 1 2 2 2 3 3 3 3 3 … ClDrw:Hist XL b

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Horiz

Horiz yValue

Draws a horizontal line on the current graph at yValue.

† GRAPH DRAW menu

IAsk

CATALOG

ident MATRX OPS menu

Horiz 4.5 b

IAsk

Sets the table so that the user can enter individual values for the independent variable.

CATALOG

IAuto

In a ZStd graph screen:

IAuto

Sets the table so that the TIN86 generates the independent-variable values automatically, based on values entered for TblStart and @Tbl. ident dimension

ident 4 b

Returns the identity matrix of dimension rows × dimension columns.

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[[1 [0 [0 [0

0 1 0 0

0 0 1 0

0] 0] 0] 1]]

Chapter 20: A to Z Function and Instruction Reference

If ‡ program editor CTL menu

:If condition :command-if-true :commands

If condition is true, executes command-if-true. Otherwise, skips command-if-true. The condition is true if it evaluates to any nonzero number, or false if it evaluates to zero.

Program segment: © :If x<0 :Disp "x is negative" ©

To execute multiple commands if condition is true, use If:Then:End instead. :If condition :Then :commands-if-true :End :commands

If condition is true (nonzero), executes commands-iftrue from Then to End. Otherwise, skips commands-iftrue and continues with the next command following End.

Program segment: © :If x<0 :Then : Disp "x is negative" : abs(x)¶x :End ©

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306

Chapter 20: A to Z Function and Instruction Reference :If condition :Then :commands-if-true :Else :commands-if-false :End :commands

If condition is true (nonzero), executes commands-iftrue from Then to Else and then continues with the next command following End.

Program segment: © :If x<0 :Then : Disp "x is negative" :Else : Disp "x is positive or zero" :End ©

If condition is false (zero), executes commands-if-false from Else to End and then continues with the next command following End.

imag CPLX menu

imag (complexNumber)

Returns the imaginary (nonreal) part of complexNumber. The imaginary part of a real number is always 0.

imag (3,4) b

4

imag (3±4) b

L2.27040748592

imag (real,imaginary) returns imaginary. imag (magnitude±angle) returns magnitude sin angle. imag complexList imag complexMatrix imag complexVector

imag {L2,(3,4),(3±4)} b {0 4 L2.27040748592}

Returns a list, matrix, or vector in which each element is the imaginary part of the original argument.

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Chapter 20: A to Z Function and Instruction Reference

InpSt ‡ program editor I/O menu

InpSt promptString,variable

Pauses a program, displays promptString, and waits for the user to enter a response. The response is stored to variable always as a string. When entering the response, the user should not enter quotation marks.

307

Program segment: © :InpSt "Enter your name:",STR ©

To prompt for a number or expression instead of a string, use Input. InpSt variable

Displays ? as the prompt.

Input ‡ program editor I/O menu

Input promptString,variable

Pauses a program, displays promptString, and waits for the user to enter a response. The response is stored to variable in the form in which the user enters it.

Program segment: © :Input "Enter test score:",SCR ©

• A number or expression is stored as a number or expression. • A list, vector, or matrix is stored as a list, vector, or matrix. • An entry enclosed in " marks is stored as a string. Input variable

Displays ? as the prompt.

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Chapter 20: A to Z Function and Instruction Reference Input

Program segment in RectGC graph format:

Pauses a program, displays the graph screen, and lets the user update x and y (or r and q in PolarGC graph format) by moving the free-moving cursor. To resume the program, press b. Input "CBLGET",variable

© :Input :Disp x,y © Input "CBLGET",L1 b

Done

Receives list data sent from a CBL or CBR System and stores it to variable on the TIN86. Use this "CBLGET" syntax for both CBL and CBR. You can receive data also by using Get( as described on page 299.

int MATH NUM menu

int number or int (expression)

Returns the largest integer  number or expression. The argument can be real or complex.

int 23.45 b

23

int L23.45 b

L24

For a negative non-integer, int returns the integer that is one less than the integer part of the number. To return the exact integer part, use iPart instead. int list int matrix int vector

Returns a list, matrix, or vector in which each element is the largest integer less than or equal to the corresponding element in the specified argument.

[[1.25,L23.45][L99,47.15]]¶MAT [[1.25 L23.45] b [L99 47.15 ]] int MAT b

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Chapter 20: A to Z Function and Instruction Reference

inter(

inter(x1,y1,x2,y2,xValue)

Calculates the line through points (x1,y1) and (x2,y2) and then interpolates or extrapolates a y value for the specified xValue.

† MATH menu

inter(y1,x1,y2,x2,yValue)

Interpolates or extrapolates an x value for the specified yValue. Notice that points (x1,y1) and (x2,y2) must be entered as (y1,x1) and (y2,x2).

Inverse:

L1

numberL1 or (expression)L1



Returns 1 divided by a real or complex number, where number ƒ 0. listL1

309

Using points (3,5) and (4,4), find the y value at x=1: inter(3,5,4,4,1) b

7

Using points (L4,L7) and (2,6), find the x value at y=10: inter(L7,L4,6,2,10) b 3.84615384615 5 L1 b (10¹6)L1

.2 b

.016666666667

{L.5,10,2/8}L1 b

{L2 .1 4}

[[1,2][3,4]]L1 b

[[L2 1 ] [1.5 L.5]]

Returns a list in which each element is 1 divided by the corresponding element in list. squareMatrixL1 Returns an inverted squareMatrix, where det ƒ 0.

iPart MATH NUM menu

iPart number or iPart (expression)

Returns the integer part of number or expression. The argument can be real or complex.

iPart 23.45 b

23

iPart L23.45 b

L23

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Chapter 20: A to Z Function and Instruction Reference iPart list iPart matrix iPart vector

Returns a list, matrix, or vector in which each element is the integer part of the corresponding element in the specified argument.

IS>( ‡ program editor CTL menu

:IS>(variable,value) :command-if-variablevalue :commands

Increments variable by 1. If the result is > value, skips command-if-variablevalue. If the result is  value, then command-if-variablevalue is executed.

[[1.25,L23.45][L99.5,47.15]]¶MAT [[1.25 L23.45] b [L99.5 47.15 ]] iPart MAT b

Program segment: © :0¶A :Lbl Start :Disp A :IS>(A,5) :Goto Start :Disp "A is now >5" ©

variable cannot be a built-in variable.

LabelOff † graph format screen

LabelOn † graph format screen

LabelOff

Turns off axes labels. LabelOn

Turns on axes labels.

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Chapter 20: A to Z Function and Instruction Reference

Lbl ‡ program editor CTL menu

Lbl label

Creates a label of up to eight characters. A program can use a Goto instruction to transfer control (branch) to a specified label. InpSt stores input as a string, so be sure to store a string to the password variable.

lcm( MATH MISC menu

LCust( ‡ program editor CTL menu

lcm(integerA,integerB)

Returns the least common multiple of two nonnegative integers. LCust(item#,"title" [,item#,"title", ...])

311

Program segment, assuming a correct password has already been stored to the password variable: © :Lbl Start :InpSt "Enter password:",PSW :If PSWƒpassword :Goto Start :Disp "Welcome" © lcm(5,2) b lcm(6,9) b lcm(18,33) b

10 18 198

Program segment:

Loads (defines) the TIN86’s custom menu, which is displayed when the user presses 9. The menu can have up to 15 items, shown in three groups of five items. For each item#/title pair:

© :LCust(1,"t",2,"Q'1",3,"Q'2",4,"R K",5,"Euler",6,"QI1",7,"QI2",8,"t Min") ©

• item# — integer from 1 through 15 that identifies the item’s position in the menu. The item numbers must be specified in order, but you can skip numbers.

After executed and when the user presses 9:

• "title" — string with up to 8 characters (not counting the quotes) that will be pasted to the current cursor location when the item is selected. This can be a variable name, expression, function name, program name, or any text string.

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Chapter 20: A to Z Function and Instruction Reference

Less than: < TEST menu

numberA < numberB or (expressionA) < (expressionB) Tests whether the condition is true or false. The arguments must be real numbers. • If true (numberA < numberB), returns 1. • If false (numberA ‚ numberB), returns 0. number < list

2<0 b

0

88<123 b

1

L5
0

(20¹5/2)<(18¹3) b

1

1<{1,L6,10} b

{0 0 1}

{1,5,9}<{1,L6,10} b

{0 0 1}

Returns a list of 1s and/or 0s to indicate if number is < the corresponding element in list. listA < listB Returns a list of 1s and/or 0s to indicate if each element in listA is < the corresponding element in listB.

Less than or equal to:  TEST menu

numberA  numberB or (expressionA)  (expressionB) Tests whether the condition is true or false. The arguments must be real numbers. • If true (numberA  numberB), returns 1. • If false (numberA > numberB), returns 0. number  list

20 b

0

88123 b

1

L5L5 b

1

(20¹5/2)(18¹3) b

1

1{1,L6,10} b

{1 0 1}

{1,5,9}{1,L6,10} b

{1 0 1}

Returns a list of 1s and/or 0s to indicate if number is  the corresponding element in list. listA  listB Returns a list of 1s and/or 0s to indicate if each element in listA is  the corresponding element in listB.

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Chapter 20: A to Z Function and Instruction Reference

LgstR STAT CALC menu Built-in equation variables such as y1, r1, and xt1 are case-sensitive. Do not use Y1, R1, and XT1. LgstR returns a tolMet value that indicates if the result meets the TI-86’s internal tolerance. • If tolMet=1, the result is within the internal tolerance. • If tolmet=0, the result is outside the internal tolerance, although it may be useful for general purposes.

LgstR [iterations,]xList,yList,frequencyList,equationVariable

Fits a logistic regression model (y=a/(1+be cx)+d) to real data pairs in xList and yList and frequencies in frequencyList. The regression equation is stored to equationVariable, which must be a built-in equation variable such as y1, r1, and xt1. The equation’s coefficients always are stored as a list to built-in variable PRegC. The number of iterations is optional. If omitted, 64 is the default. A large number of iterations may produce more accurate results but may require longer calculation times. A smaller number may produce less accurate results but with shorter calculation times.

313

In Func graphing mode: {1,2,3,4,5,6}¶L1 b {1 2 3 4 5 6} {1,1.3,2.5,3.5,4.5,4.8}¶L2 b {1 1.3 2.5 3.5 4.5 4… LgstR L1,L2,y1 b

Plot1(1,L1,L2) b ZData b

Values used for xList, yList, and frequencyList are stored automatically to built-in variables xStat, yStat, and fStat, respectively. The regression equation is stored also to built-in equation variable RegEq. LgstR [iterations,]xList,yList,equationVariable

Uses frequencies of 1. LgstR [iterations,]xList,yList,frequencyList

Stores the regression equation to RegEq only. LgstR [iterations,]xList,yList

Uses frequencies of 1, and stores the regression equation to RegEq only.

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Done

314

Chapter 20: A to Z Function and Instruction Reference LgstR [iterations,]equationVariable

Uses xStat, yStat, and fStat for xList, yList, and frequencyList, respectively. These built-in variables must contain valid data of the same dimension; otherwise, an error occurs. The regression equation is stored to equationVariable and RegEq. LgstR [iterations]

Uses xStat, yStat, and fStat, and stores the regression equation to RegEq only.

Line( † GRAPH DRAW menu

Line(x1,y1,x2,y2)

Draws a line from point (x1,y1) to (x2,y2).

In Func graphing mode and a ZStd graph screen: Line(L2,L7,9,8) b

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Chapter 20: A to Z Function and Instruction Reference

LinR STAT CALC menu

Built-in equation variables such as y1, r1, and xt1 are case-sensitive. Do not use Y1, R1, and XT1.

LinR xList,yList,frequencyList,equationVariable

Fits a linear regression model (y=a+bx) to real data pairs in xList and yList and frequencies in frequencyList. The regression equation is stored to equationVariable, which must be a built-in equation variable such as y1, r1, and xt1.

315

In Func graphing mode: {1,2,3,4,5,6}¶L1 b {1 2 3 4 5 6} {4.5,4.6,6,7.5,8.5,8.7}¶L2 b {4.5 4.6 6 7.5 8.5 8.7} LinR L1,L2,y1 b

Values used for xList, yList, and frequencyList are stored automatically to built-in variables xStat, yStat, and fStat, respectively. The regression equation is stored also to built-in equation variable RegEq. LinR xList,yList,equationVariable

Uses frequencies of 1.

Plot1(1,L1,L2) b ZData b

LinR xList,yList,frequencyList

Stores the regression equation to RegEq only. LinR xList,yList

Uses frequencies of 1, and stores the regression equation to RegEq only. LinR equationVariable

Uses xStat, yStat, and fStat for xList, yList, and frequencyList, respectively. These built-in variables must contain valid data of the same dimension; otherwise, an error occurs. The regression equation is stored to equationVariable and RegEq.

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316

Chapter 20: A to Z Function and Instruction Reference LinR

Uses xStat, yStat, and fStat, and stores the regression equation to RegEq only.

List entry: { } LIST menu

li4vc LIST OPS menu

{element1,element2, ...}

Defines a list in which each element is a real or complex number or variable. li4vc list

{1,2,3}¶L1 b

{1 2 3}

In RectC complex number mode: {3,(2,4),8¹2}¶L2 b {(3,0) (2,4) (16,0)} li4vc {2,7,L8,0} b [2 7 L8 0]

Returns a vector converted from a real or complex list.

VECTR OPS menu

ln B

ln number or ln (expression)

Returns the natural logarithm of a real or complex number or expression. ln list

Returns a list in which each element is the natural logarithm of the corresponding element in list.

lngth STRNG menu

lngth string

Returns the length (number of characters) of string. The character count includes spaces but not quotation marks.

ln 2 b

.69314718056

ln (36.4/3) b

2.49595648597

In RectC complex number mode: ln L3 b

(1.09861228867,3.141…

ln {2,3} b {.69314718056 1.0986… lngth "The answer is:" b

14

"The answer is:"¶STR b The answer is: lngth STR b 14

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Chapter 20: A to Z Function and Instruction Reference

LnR STAT CALC menu

Built-in equation variables such as y1, r1, and xt1 are case-sensitive. Do not use Y1, R1, and XT1.

LnR xList,yList,frequencyList,equationVariable

Fits a logarithmic regression model (y=a+b ln x) to the real data pairs in xList and yList (x values must be > 0) and frequencies in frequencyList. The regression equation is stored to equationVariable, which must be a built-in equation variable such as y1, r1, and xt1.

317

In Func graphing mode: {1,2,3,4,5,6}¶L1 b {1 2 3 4 5 6} {.6,1.5,3.8,4.2,4.3,5.9}¶L2 b {.6 1.5 3.8 4.2 4.3 5.9} LnR L1,L2,y1 b

Values used for xList, yList, and frequencyList are stored automatically to built-in variables xStat, yStat, and fStat, respectively. The regression equation is stored also to built-in equation variable RegEq. LnR xList,yList,equationVariable

Uses frequencies of 1.

Plot1(1,L1,L2) b ZData b

LnR xList,yList,frequencyList

Stores the regression equation to RegEq only. LnR xList,yList

Uses frequencies of 1, and stores the regression equation to RegEq only. LnR equationVariable

Uses xStat, yStat, and fStat for xList, yList, and frequencyList, respectively. These built-in variables must contain valid data of the same dimension; otherwise, an error occurs. The regression equation is stored to equationVariable and RegEq.

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Done

318

Chapter 20: A to Z Function and Instruction Reference LnR

Uses xStat, yStat, and fStat, and stores the regression equation to RegEq only.

log <

log number or log (expression)

Returns the logarithm of a real or complex number or expression, where: 10

logarithm

= number

log list

Returns a list in which each element is the logarithm of the corresponding element in list.

LU( MATRX MATH menu

LU(matrix,lMatrixName, uMatrixName, pMatrixName)

Calculates the Crout LU (lower-upper) decomposition of a real or complex matrix. The lower triangular matrix is stored in lMatrixName, the upper triangular matrix in uMatrixName, and the permutation matrix (which describes the row swaps done during the calculation) in pMatrixName. lMatrixName ¹ uMatrixName = pMatrixName ¹ matrix

log 2 b log (36.4/3) b

.301029995664 1.08398012893

In RectC complex number mode: log (3,4) b (.698970004336,.4027… In RectC complex number mode: log {L3,2} b {(.47712125472,1.364… [[6,12,18][5,14,31][3,8,18]] [[6 12 18] ¶MAT b [5 14 31] [3 8 18]] LU(MAT,L,U,P) b

Done

L b

[[6 0 0] [5 4 0] [3 2 1]]

U b

[[1 2 3] [0 1 4] [0 0 1]]

P b

[[1 0 0] [0 1 0] [0 0 1]]

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Chapter 20: A to Z Function and Instruction Reference

Matrix entry: [ ] - „ and - …

[ [row1] [row2] ... ]

Defines a matrix entered row-by-row in which each element is a real or complex number or variable.

319

[[1,2,3][4,5,6]]¶MAT b [[1 2 3] [4 5 6]]

Enter each [row] as [element,element, ... ].

max( MATH NUM menu

max(numberA,numberB)

max(2.3,1.4) b

2.3

Returns the larger of two real or complex numbers. max(list)

max({1,9,p/2,e^2}) b

9

Returns the largest element in list. max(listA,listB)

max({1,10},{2,9}) b

{2 10}

Returns a list in which each element is the larger of the corresponding elements in listA and listB.

MBox † STAT DRAW menu

MBox xList,frequencyList

Draws a modified box plot on the current graph, using the real data in xList and the frequencies in frequencyList. MBox xList

Starting with a ZStd graph screen: {1,2,3,4,5,9}¶XL b {1 2 3 4 5 9} {1,1,1,4,1,1}¶FL b {1 1 1 4 1 1} 0¶xMin:0¶yMin b 0 MBox XL,FL b

Uses frequencies of 1. MBox

Uses the data in built-in variables xStat and fStat. These variables must contain valid data of the same dimension; otherwise, an error occurs.

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Chapter 20: A to Z Function and Instruction Reference

Menu( ‡ program editor CTL menu

Menu(item#,"title1",label1[, ... ,item#,"title15",label15])

Generates a menu of up to 15 items during program execution. Menus are displayed as three groups of five items. For each item: • item# — integer from 1 through 15 that identifies this item’s position in the menu. • "title" — text string that will be displayed for this item on the menu. Typically, use from 1 through 5 characters; additional characters may not be seen on the menu.

Program segment: © :Lbl A :Input "Radius:",RADIUS :Disp "Area is:",p¹RADIUS 2 :Menu(1,"Again",A,5,"Stop",B) :Lbl B :Disp "The End" Example when executed:

• label — valid label to which program execution will branch when the user selects this item.

min( MATH NUM menu

min(numberA,numberB)

Returns the smaller of two real or complex numbers. min(list)

min(3,L5) b min(L5.2, L5.3) b min(5,2+2) b min({1,3,L5}) b

L5 L5.3 4

L5

Returns the smallest element in list. min(listA,listB)

min({1,2,3},{3,2,1}) b {1 2 1}

Returns a list in which each element is the smaller of the corresponding elements in listA and listB.

mod( MATH NUM menu

mod(numberA,numberB)

Returns numberA modulo numberB. The arguments must be real.

mod(7,0) b mod(7,3) b mod(L7,3) b mod(7,L3) b mod(L7,L3) b

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7 1 2 L2 L1

Chapter 20: A to Z Function and Instruction Reference

mRAdd( MATRX OPS menu

mRAdd(number,matrix,rowA,rowB)

Returns the result of a “multiply and add row” matrix operation, where: a. rowA of a real or complex matrix is multiplied by a real or complex number.

[[5,3,1][2,0,4][3,L1,2]]¶MAT [[5 3 1] b [2 0 4] [3 L1 2]] mRAdd(5,MAT,2,3) b [[5 3 1 ] [2 0 4 ] [13 L1 22]]

b. The results are added to (and then stored in) rowB.

Multiplication: ¹ M

numberA ¹ numberB

321

2¹5 b

10

Returns the product of two real or complex numbers. number ¹ list or list ¹ number number ¹ matrix or matrix ¹ number number ¹ vector or vector ¹ number Returns a list, matrix, or vector in which each element is number multiplied by the corresponding element in list, matrix, or vector. listA ¹ listB

4¹{10,9,8} b

{40 36 32}

In RectC complex number mode: [8,1,(5,2)]¹3 b [(24,0) (3,0) (15,6)]

{1,2,3}¹{4,5,6} b

{4 10 18}

Returns a list in which each element of listA is multiplied by the corresponding element of listB. The lists must have the same dimension. matrix ¹ vector Returns a vector in which matrix is multiplied by vector. The number of columns in matrix must equal the number of elements in vector.

[[1,2,3][4,5,6]]¶MAT b [[1 2 3] [4 5 6]] MAT¹[7,8,9] b [50 122]

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Chapter 20: A to Z Function and Instruction Reference matrixA ¹ matrixB Returns a matrix in which matrixA is multiplied by matrixB. The number of columns in matrixA must equal the number of rows in matrixB.

[[2,2][3,4]]¶MATA b

[[1,2,3][4,5,6]]¶MATB b [[1 2 3] [4 5 6]] MATA¹MATB b

multR( MATRX OPS menu

multR(number,matrix,row)

Returns the result of a “row multiplication” matrix operation, where: a. The specified row of a real or complex matrix is multiplied by a real or complex number.

MATH PROB menu

items nCr number

[[10 14 18] [19 26 33]]

[[5,3,1][2,0,4][3,L1,2]]¶MAT b [[5 3 1] [2 0 4] [3 L1 2]] multR(5,MAT,2) b [[5 3 1 ] [10 0 20] [3 L1 2 ]]

b. The results are stored in the same row.

nCr

[[2 2] [3 4]]

5 nCr 2 b

Returns the number of combinations of items (n) taken number (r) at a time. Both arguments must be real nonnegative integers.

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Chapter 20: A to Z Function and Instruction Reference

nDer( CALC menu

To view or set the value for d, press - ™ ) to display the tolerance screen.

nDer(expression,variable,value)

Returns an approximate numerical derivative of expression with respect to variable evaluated at a real or complex value. The approximate numerical derivative is the slope of the secant line through the points:

nDer(x^3,x,5) b

75.000001

For d=1EL4: nDer(x^3,x,5) b

75

5¶x b nDer(x^3,x) b

5 75

(valueNd,f(valueNd)) and (value+d,f(value+d))

Uses the current value of variable.

a

For d=.001:

As the step value d gets smaller, the approximation usually gets more accurate. nDer(expression,variable)

Negation: L

323

L number or L (expression) L list L matrix L vector

L2+5 b

3

L(2+5) b

L7

L{0,L5,5} b

{0 5 L5}

Returns the negative of the real or complex argument.

norm MATRX MATH menu VECTR MATH menu

norm matrix

Returns the Frobenius norm of a real or complex matrix, calculated as:

[[1,L2][L3,4]]¶MAT b norm MAT b

G(real 2+imaginary 2) where the sum is over all elements.

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[[1 L2] [L3 4 ]] 5.47722557505

324

Chapter 20: A to Z Function and Instruction Reference norm [3,4,5] b

norm vector

7.07106781187

Returns the length of a real or complex vector, where: norm [a,b,c] returns

a 2+b 2+c 2.

norm number or norm (expression) norm list

Returns the absolute value of a real or complex number or expression, or of each element in list.

Normal † mode screen

Normal

Sets normal notation mode.

norm L25 b

25

In Radian angle mode: norm {L25,cos L(p/3)} b {25 .5} In Eng notation mode: 123456789 b

123.456789E6

In Sci notation mode: 123456789 b

1.23456789E8

In Normal notation mode: 123456789 b

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123456789

Chapter 20: A to Z Function and Instruction Reference

not BASE BOOL menu

not integer

325

In Dec number base mode:

Returns the one’s complement of a real integer. Internally, integer is represented as a 16-bit binary number. The value of each bit is flipped (0 becomes 1, and vice versa) for the one’s complement. For example, not 78: 78 = 0000000001001110Ü 1111111110110001Ü (one’s complement)

not 78 b

L79

In Bin number base mode: not 1001110 b Ans4Dec b

Sign bit; 1 indicates a negative number

To find the magnitude of a negative binary number, determine its two’s complement (take the one’s complement and then add 1). For example: 1111111110110001Ü = one’s complement of 78 0000000001001110Ü (one’s complement) + 0000000000000001Ü 0000000001001111Ü = 79 (two’s complement) Therefore, not 78 = L79. You can enter real numbers instead of integers, but they are truncated automatically before the comparison.

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1111111110110001Ü L79Þ

326

Chapter 20: A to Z Function and Instruction Reference

Not equal to: ƒ TEST menu

numberA ƒ numberB matrixA ƒ matrixB vectorA ƒ vectorB stringA ƒ stringB Tests whether the condition argumentA ƒ argumentB is true or false. Numbers, matrices, and vectors can be real or complex. If complex, the magnitude (modulus) of each element is compared. Strings are case-sensitive.

2+2ƒ3+2 b

1

2+(2ƒ3)+2 b

5

[1,2]ƒ[3N2,L1+3] b

0

"A"ƒ"a" b

1

• If true (argumentA ƒ argumentB), returns 1. • If false (argumentA = argumentB), returns 0. listA ƒ listB

{1,5,9}ƒ{1,L6,9} b

{0 1 0}

Returns a list of 1s and/or 0s to indicate if each element in listA is ƒ the corresponding element in listB.

nPr MATH PROB menu

Ý

items nPr number

20

Returns the number of permutations of items (n) taken number (r) at a time. Both arguments must be real nonnegative integers. integer Ý

BASE TYPE menu

5 nPr 2 b

Designates a real integer as octal, regardless of the number base mode setting.

In Dec number base mode: 10Ý b 10Ý+10 b

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Chapter 20: A to Z Function and Instruction Reference

Oct † mode screen

4Oct BASE CONV menu

Oct

In Oct number base mode:

Sets octal number base mode. Results are displayed with the Ý suffix. In any number base mode, you can designate an appropriate value as binary, decimal, hexadecimal, or octal by using the Ü, Þ, ß, or Ý designator, respectively, from the BASE TYPE menu. number 4Oct list 4Oct matrix 4Oct vector 4Oct Returns the octal equivalent of the real or complex argument.

OneVar STAT CALC menu (OneVa shows on menu)

327

OneVar xList,frequencyList

Performs one-variable statistical analysis using real data points in xList and frequencies in frequencyList.

10+10Ü+Úß+10Þ b

In Dec number base mode: 2¹8 b Ans4Oct b

16 20Ý

{7,8,9,10}4Oct b {7Ý 10Ý 11Ý 12Ý}

{0,1,2,3,4,5,6}¶XL b {0 1 2 3 4 5 6} OneVar XL b

The values used for xList and frequencyList are stored automatically to built-in variables xStat and fStat, respectively. OneVar xList

Uses frequencies of 1.

43Ý

Scroll down to see more results.

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Chapter 20: A to Z Function and Instruction Reference OneVar

Uses xStat and fStat for xList and frequencyList. These built-in variables must contain valid data of the same dimension; otherwise, an error occurs.

or BASE BOOL menu

integerA or integerB Compares two real integers bit by bit. Internally, both integers are converted to binary. When corresponding bits are compared, the result is 1 if either bit is 1; the result is 0 only if both bits are 0. The returned value is the sum of the bit results. For example, 78 or 23 = 95.

In Dec number base mode: 78 or 23 b

95

In Bin number base mode: 1001110 or 10111 b Ans4Dec b

78 = 1001110Ü 23 = 0010111Ü 1011111Ü = 95 You can enter real numbers instead of integers, but they are truncated automatically before the comparison.

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1011111Ü 95Þ

Chapter 20: A to Z Function and Instruction Reference

Outpt( ‡ program editor I/O menu

Outpt(row,column,string)

Displays string beginning at row and column, where 1  row  8 and 1  column  21. Outpt(row,column,value)

Displays value beginning at the specified row and column.

Program segment: © :ClLCD :For(i,1,8) : Outpt(i,randInt(1,21),"A") :End © Example result after execution:

Outpt("CBLSEND",listName)

Sends the contents of listName to the CBL or CBR System. You can send data also by using Send( as described on page 350.

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P2Reg STAT CALC menu

Built-in equation variables such as y1, r1, and xt1 are case-sensitive. Do not use Y1, R1, and XT1.

P2Reg xList,yList,frequencyList,equationVariable

Performs a second order polynomial regression using real data pairs in xList and yList and frequencies in frequencyList. The regression equation is stored to equationVariable, which must be a built-in equation variable such as y1, r1, and xt1. The equation’s coefficients always are stored as a list to built-in variable PRegC. Values used for xList, yList, and frequencyList are stored automatically to built-in variables xStat, yStat, and fStat, respectively. The regression equation is stored also to built-in equation variable RegEq.

In Func graphing mode: {1,2,3,4,5,6}¶L1 b {1 2 3 4 5 6} {L2,6,11,23,29,47}¶L2 b {L2 6 11 23 29 47} P2Reg L1,L2,y1 b

Plot1(1,L1,L2) b ZData b

P2Reg xList,yList,equationVariable

Uses frequencies of 1. P2Reg xList,yList,frequencyList

Stores the regression equation to RegEq only. P2Reg xList,yList

Uses frequencies of 1, and stores the regression equation to RegEq only. P2Reg equationVariable

Uses xStat, yStat, and fStat for xList, yList, and frequencyList, respectively. These built-in variables must contain valid data of the same dimension; otherwise, an error occurs. The regression equation is stored to equationVariable and RegEq.

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Chapter 20: A to Z Function and Instruction Reference

331

P2Reg

Uses xStat, yStat, and fStat, and stores the regression equation to RegEq only.

P3Reg STAT CALC menu

Built-in equation variables such as y1, r1, and xt1 are case-sensitive. Do not use Y1, R1, and XT1.

P3Reg xList,yList,frequencyList,equationVariable

Performs a third order polynomial regression using real data pairs in xList and yList and frequencies in frequencyList. The regression equation is stored to equationVariable, which must be a built-in equation variable such as y1, r1, and xt1. The equation’s coefficients always are stored as a list to built-in variable PRegC. Values used for xList, yList, and frequencyList are stored automatically to built-in variables xStat, yStat, and fStat, respectively. The regression equation is stored also to built-in equation variable RegEq.

In Func graphing mode: {1,2,3,4,5,6}¶L1 b {1 2 3 4 5 6} {L6,15,27,88,145,294}¶L2 b {L6 15 27 88 145 294} P3Reg L1,L2,y1 b

Plot1(1,L1,L2) b ZData b

P3Reg xList,yList,equationVariable

Uses frequencies of 1. P3Reg xList,yList,frequencyList

Stores the regression equation to RegEq only. P3Reg xList,yList

Uses frequencies of 1, and stores the regression equation to RegEq only.

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Chapter 20: A to Z Function and Instruction Reference P3Reg equationVariable

Uses xStat, yStat, and fStat for xList, yList, and frequencyList, respectively. These built-in variables must contain valid data of the same dimension; otherwise, an error occurs. The regression equation is stored to equationVariable and RegEq. P3Reg

Uses xStat, yStat, and fStat, and stores the regression equation to RegEq only.

P4Reg STAT CALC menu

Built-in equation variables such as y1, r1, and xt1 are case-sensitive. Do not use Y1, R1, and XT1.

P4Reg xList,yList,frequencyList,equationVariable

Performs a fourth order polynomial regression using real data pairs in xList and yList and frequencies in frequencyList. The regression equation is stored to equationVariable, which must be a built-in equation variable such as y1, r1, and xt1. The equation’s coefficients always are stored as a list to built-in variable PRegC. Values used for xList, yList, and frequencyList are stored automatically to built-in variables xStat, yStat, and fStat, respectively. The regression equation is stored also to built-in equation variable RegEq.

In Func graphing mode: {L2,L1,0,1,2,3,4,5,6}¶L1 b {L2 L1 0 1 2 3 4 5 6} {4,3,1,2,3,2,2,4,6}¶L2 b {4 3 1 2 3 2 2 4 6} P4Reg L1,L2,y1 b

Plot1(1,L1,L2) b ZData b

P4Reg xList,yList,equationVariable

Uses frequencies of 1. P4Reg xList,yList,frequencyList

Stores the regression equation to RegEq only.

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P4Reg xList,yList

Uses frequencies of 1, and stores the regression equation to RegEq only. P4Reg equationVariable

Uses xStat, yStat, and fStat for xList, yList, and frequencyList, respectively. These built-in variables must contain valid data of the same dimension; otherwise, an error occurs. The regression equation is stored to equationVariable and RegEq. P4Reg

Uses xStat, yStat, and fStat, and stores the regression equation to RegEq only.

Param † mode screen

Pause ‡ program editor CTL menu

Param

Sets parametric graphing mode. Pause string Pause value Pause list Pause matrix Pause vector

Displays the specified argument and then suspends program execution until the user presses b.

Program segment: © :Input "Enter x:",x :y1=x 2N6 :Disp "y1 is:",y1 :Pause "Press ENTER to graph" :ZStd ©

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Chapter 20: A to Z Function and Instruction Reference Pause

Suspends program execution until the user presses b.

Percent: %

number% or (expression)% Returns a real number or expression divided by 100.

MATH MISC menu

pEval(

pEval(coefficientList,xValue)

Returns the value of a polynomial (whose coefficients are given in coefficientList) at xValue.

MATH MISC menu

PlOff

PlOff [1,2,3]

5% b 5%¹200 b (10+5)%¹200 b

.05 10 30

Evaluate y=2x 2+2x+3 at x=5: pEval({2,2,3},5) b

63

PlOff 1,3 b

Done

PlOff b

Done

PlOn 2,3 b

Done

PlOn b

Done

Deselects the specified stat plot numbers.

STAT PLOT menu

PlOff

Deselects all stat plot numbers.

PlOn

PlOn [1,2,3]

Selects the specified stat plot numbers, in addition to any plot numbers that are already selected.

STAT PLOT menu

PlOn

Selects all stat plot numbers.

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Chapter 20: A to Z Function and Instruction Reference

Plot1( Plot2( Plot3( † STAT PLOT menu The syntax and descriptions to the right refer to Plot1(, but they apply as well to Plot2( and Plot3(.

Scatter plot ® Plot1(1,xListName,yListName,mark) Plot1(1,xListName,yListName) Defines and selects the plot using real data pairs in xListName and yListName.

{L9,L6,L4,L1,2,5,7,10}¶L1 b {L9 L6 L4 L1 2 5 7 1… {L7,L6,L2,1,3,6,7,9}¶L2 b {L7 L6 L2 1 3 6 7 9} Plot1(1,L1,L2) b Done ZStd b

The optional mark specifies the character used to plot the points. If you omit mark, a box is used. mark:

335

1 = box (›) 2 = cross (+) 3 = dot (¦)

xyLine plot − Plot1(2,xListName,yListName,mark) Plot1(2,xListName,yListName) Modified box plot ¯ Plot1(3,xListName,1 or frequencyListName,mark) Plot1(3,xListName,1 or frequencyListName) Plot1(3,xListName) Defines and selects the plot using real data points in xListName with the specified frequencies. If you omit 1 or frequencyListName, frequencies of 1 are used. Histogram ¬ Plot1(4,xListName,1 or frequencyListName) Plot1(4,xListName) Box plot ° Plot1(5,xListName,1 or frequencyListName) Plot1(5,xListName)

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Pol † mode screen

4Pol CPLX menu

Pol

Sets polar graphing mode. complexNumber 4Pol Displays complexNumber in polar form (magnitudeangle), regardless of the complex number mode. list 4Pol matrix 4Pol vector 4Pol Returns a list, matrix, or vector in which each element of the argument is displayed in polar form.

PolarC † mode screen

Polar complex:  -

PolarGC † graph format screen

PolarC

Sets polar complex number mode (magnitudeangle). magnitudeangle Used to enter complex numbers in polar form. The angle is interpreted according to the current angle mode.

In RectC complex number mode: ‡L2 b Ans4Pol b

(0,1.41421356237) (1.41421356237±1.570…

{1,‡L2} b {(1,0) (0,1.141421356… Ans4Pol b {(1±0) (1.4142135623…

In PolarC complex number mode: ‡L2 b

(1.41421356237±1.570…

In Radian angle mode and PolarC complex number mode: (1,2)+(3p/4) b (5.16990542093.9226…

PolarGC

Displays graph coordinates in polar form.

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poly †-v

poly coefficientList

Returns a list containing the real and complex roots of a polynomial whose coefficients are given in coefficientList.

Find the roots of 2x 3N8x 2N14x+20=0: poly {2,L8,L14,20} b {5 L2 1}

a nx n + ... + a 2x 2 + a 1x 1 + a 0x 0 = 0

Power: ^ @

number^power or (expression)^(expression) Returns number raised to power. The arguments can be real or complex.

4^2 b 2^L5 b

{8 81 1024}

Returns a list in which each element of listA is raised to the power specified by the corresponding element in listB. squareMatrix^power

[[2,3][4,5]]^3 b [[116 153] [204 269]]

Returns a matrix equivalent to squareMatrix multiplied by itself power number of times, where 0  power  255. This is not the same as simply raising each element to power.

-z

10^power

.03125

{2,3,4}^{3,4,5} b

listA^listB

Power of 10: 10^

16

or

10^(expression)

Returns 10 raised to power or expression, which can be real or complex.

10^1.5 10^L2

b

b

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31.6227766017 .01

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Chapter 20: A to Z Function and Instruction Reference 10^list

10^{1.5,L2}

Returns a list in which each element is 10 raised to the power specified by the corresponding element in list.

prod LIST OPS menu MATH MISC menu

Prompt ‡ program editor I/O menu (Promp shows on menu)

PtChg( † GRAPH DRAW menu

PtOff( † GRAPH DRAW menu

PtOn( † GRAPH DRAW menu

prod list

Returns the product of all real or complex elements in list. Prompt variableA[,variableB, ...]

Prompts the user to enter a value for variableA, then variableB, and so on.

PtChg(x,y)

prod {1,2,4,8} b prod {2,7,L8} b

Program segment: © :Prompt A,B,C ©

PtChg(L6,2)

Reverses the point at graph coordinates (x,y). PtOff(x,y)

PtOff(3,5)

Erases the point at graph coordinates (x,y). PtOn(x,y)

b {31.6227766017 .01}

PtOn(3,5)

Draws the point at graph coordinates (x,y).

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PwrR STAT CALC menu

Built-in equation variables such as y1, r1, and xt1 are case-sensitive. Do not use Y1, R1, and XT1.

PwrR xList,yList,frequencyList,equationVariable

Fits a power regression model (y=ax b) to positive real data pairs in xList and yList, using frequencies in frequencyList. The regression equation is stored to equationVariable, which must be a built-in equation variable such as y1, r1, and xt1.

339

In Func graphing mode: {1,2,3,4,5,6}¶L1 b {1 2 3 4 5 6} {1,17,21,52,75,133}¶L2 b {1 17 21 52 75 133} PwrR L1,L2,y1 b

Values used for xList, yList, and frequencyList are stored automatically to built-in variables xStat, yStat, and fStat, respectively. The regression equation is stored also to built-in equation variable RegEq. PwrR xList,yList,equationVariable

Uses frequencies of 1.

Plot1(1,L1,L2) b ZData b

PwrR xList,yList,frequencyList

Stores the regression equation to RegEq only. PwrR xList,yList

Uses frequencies of 1, and stores the regression equation to RegEq only. PwrR equationVariable

Uses xStat, yStat, and fStat for xList, yList, and frequencyList, respectively. These built-in variables must contain valid data of the same dimension; otherwise, an error occurs. The regression equation is stored to equationVariable and RegEq.

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Chapter 20: A to Z Function and Instruction Reference PwrR

Uses xStat, yStat, and fStat, and stores the regression equation to RegEq only.

PxChg( GRAPH DRAW menu

PxOff( GRAPH DRAW menu

PxOn( GRAPH DRAW menu

PxTest( GRAPH DRAW menu

rAdd( MATRX OPS menu

PxChg(row,column)

PxChg(10,95)

Reverses the pixel at (row, column), where 0  row  62 and 0  column  126. PxOff(row,column)

PxOff(10,95)

Erases the pixel at (row, column), where 0  row  62 and 0  column  126. PxOn(row,column)

PxOn(10,95)

Draws the pixel at (row, column), where 0  row  62 and 0  column  126. PxTest(row,column)

Returns 1 if the pixel at (row, column) is on, 0 if it is off; 0  row  62 and 0  column  126. rAdd(matrix,rowA,rowB)

Returns a matrix in which rowA of a real or complex matrix is added to (and stored in) rowB.

Assuming the pixel at (10,95) is already on: PxTest(10,95) b

1

[[5,3,1][2,0,4][3,L1,2]]¶MAT [[5 3 1] b [2 0 4] [3 L1 2]] rAdd(MAT,2,3) b

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[[5 3 1] [2 0 4] [5 L1 6]]

Chapter 20: A to Z Function and Instruction Reference

Radian

Radian

†-m

Radian entry:

Sets radian angle mode. r

number r or (expression) r Designates a real number or expression as radians, regardless of the angle mode setting.

MATH ANGLE menu

list r

341

In Radian angle mode: sin (p/2) b sin 90 b

1 .893996663601

In Degree angle mode: cos (p/2) b cos (p/2) r b

.999624216859 0

cos {p/2,p}r b

{0 L1}

Designates each element in a real list as radians.

rand MATH PROB menu

rand

Returns a random number between 0 and 1. To control a random number sequence, first store an integer seed value to rand (such as 0¶rand).

randBin( MATH PROB menu (randBi shows on menu)

randBin(#ofTrials,probabilityOfSuccess,#ofSimulations)

Returns a list of random integers from a binomial distribution, where #ofTrials ‚ 1 and 0  probabilityOfSuccess  1. The #ofSimulations is an integer ‚ 1 that specifies the number of integers returned in the list.

You may have different results for the first two examples: rand b rand b

.943597402492 .146687829222

0¶rand:rand b 0¶rand:rand b

.943597402492 .943597402492

1¶rand:randBin(5,.2,3) b {0 3 2}

A seed value stored to rand also affects randBin(. randBin(#ofTrials,probabilityOfSuccess)

0¶rand:randBin(5,.2) b

Returns a single random integer.

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1

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Chapter 20: A to Z Function and Instruction Reference

randInt( MATH PROB menu (randIn shows on menu)

randInt(lower,upper,#ofTrials)

Returns a list of random integers bound by the specified integers, lower  integer  upper. The #ofTrials is an integer ‚ 1 that specifies the number of integers returned in the list.

1¶rand:randInt(1,10,3) b {8 9 3}

A seed value stored to rand also affects randInt(. randInt(lower,upper)

0¶rand:randInt(1,10) b

10

Returns a single random integer.

randM( MATRX OPS menu

randNorm( MATH PROB menu (randN shows on menu)

randM(rows,columns)

0¶rand:randM(2,3) b [[4 L2 0] [L7 8 8]]

Returns a rows × columns matrix filled with random one-digit integers (L9 to 9). randNorm(mean,stdDeviation,#ofTrials)

Returns a list of random numbers from a normal distribution specified by mean and stdDeviation. The #ofTrials is an integer ‚ 1 that specifies how many numbers are returned. Each returned number could be any real number, but most will be within the interval:

1¶rand:randNorm(0,1,3) b {L.660585055265 L1.0…

[meanN3(stdDeviation), mean+3(stdDeviation)]. A seed value stored to rand also affects randNorm(. randNorm(mean,stdDeviation)

Returns a single random number.

0¶rand:randNorm(0,1) b L1.58570962271

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Chapter 20: A to Z Function and Instruction Reference

RcGDB † GRAPH menu

RcPic † GRAPH menu

real CPLX menu

343

RcGDB graphDataBaseName

Restores all settings stored in graphDataBaseName. For a list of settings, refer to StGDB on page 361. RcPic pictureName

Displays the current graph and adds the picture stored in pictureName. real (complexNumber)

Returns the real part of complexNumber. real (real,imaginary) returns real. real (magnitude±angle) returns magnitude ¹cos (angle). real complexList real complexMatrix real complexVector

In Radian angle mode: real (3,4) b

3

real (3±4) b

L1.96093086259

In Radian angle mode: real {L2,(3,4),(3±4)} b {L2 3 L1.96093086259}

Returns a list, matrix, or vector in which each element is the real part of the corresponding element in the argument.

4Rec CPLX menu

complexNumber 4Rec Displays complexNumber in rectangular form (real,imaginary) regardless of the complex number mode.

In PolarC complex number mode: ‡L2 b (1.41421356237±1.570… Ans4Rec b (0,1.41421356237)

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Chapter 20: A to Z Function and Instruction Reference complexList 4Rec complexMatrix 4Rec complexVector 4Rec Returns a list, matrix, or vector in which each element of the argument is displayed in rectangular form.

RectC † mode screen

RectGC † graph format screen

RectV † mode screen

ref MATRX OPS menu

RectC

Sets rectangular complex number mode (real,imaginary).

In PolarC complex number mode: [(3±p/6),‡L2] b [(3±.523598775598) (… Ans4Rec b [(2.59807621135,1.5)…

In RectC complex number mode: ‡L2 b

(0,1.41421356237)

RectGC

Displays graph coordinates in rectangular form. RectV

Sets rectangular vector coordinate mode [x y z]. ref matrix

Returns the row-echelon form of a real or complex matrix. The number of columns must be greater than or equal to the number of rows.

In RectV vector coordinate mode: 3¹[4±5] b [3.40394622556 L11.5… [[4,5,6][7,8,9]]¶MAT b [[4 5 [7 8 ref MAT b [[1 1.14285714286 [0 1

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6] 9]] 1.… 2 …

Chapter 20: A to Z Function and Instruction Reference

Repeat ‡ program editor CTL menu (Repea shows on menu)

Return

:Repeat condition :commands-to-repeat :End :commands

Executes commands-to-repeat until condition is true.

Return

In a subroutine, exits the subroutine and returns to the calling program. In the main program, stops execution and returns to the home screen.

‡ program editor CTL menu (Retur shows on menu)

Program segment: © :6¶N :1¶Fact :Repeat N<1 : Fact¹N¶Fact : NN1¶N :End :Disp "6!=",Fact © Program segment in the calling program: © :Input "Diameter:",DIAM :Input "Height:",HT :AREACIRC :VOL=AREA¹HT :Disp "Volume =",VOL © AREACIRC subroutine program: PROGRAM:AREACIRC :RADIUS=DIAM/2 :AREA=p¹RADIUS 2 :Return

RK † graph format screen (scroll down to second screen)

345

RK

In DifEq graphing mode, uses an algorithm based on the Runge-Kutta method to solve differential equations. Typically, RK is more accurate than Euler but takes longer to find the solutions.

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rnorm MATRX MATH menu

rnorm matrix

Returns the row norm of a real or complex matrix. For each row, rnorm sums the absolute values (magnitudes of complex elements) of all elements on that row. The returned value is the largest of the sums.

[[L5,6,L7][3,3,9][9,L9,L7]] [[L5 6 L7] ¶MAT b [3 3 9 ] [9 L9 L7]] rnorm MAT b 25 rnorm [15,L18,7] b

rnorm vector

18

Returns the largest absolute value (or magnitude) in a real or complex vector. x

Root: ‡ MATH MISC menu

x throot x‡number or x throot x‡(expression)

5x‡32 b

2

th

Returns the x root of number or expression. The arguments can be real or complex. x throot x‡list

5x‡{32,243} b

{2 3}

{5,2}x‡{32,25) b

{2 5}

th

Returns a list in which each element is the x root of the corresponding element in list. x throotList x‡list Returns a list in which each element is the root specified by the corresponding elements in x throotList and list.

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Chapter 20: A to Z Function and Instruction Reference

rotL BASE BIT menu

rotL integer

Returns a real integer with bits rotated one to the left. Internally, integer is represented as a 16-bit binary number. When the bits are rotated left, the leftmost bit rotates to the rightmost bit.

347

In Bin number base mode: rotL 0000111100001111 b 1111000011110Ü Leading zeros are not displayed.

rotL 0000111100001111Ü = 0001111000011110Ü

rotL is not valid in Dec number base mode. To enter hexadecimal numbers Õ through Ú, use the BASE A-F menu. Do not use 1 to type a letter.

rotR BASE BIT menu

rotR integer

Returns a real integer with bits rotated one to the right. Internally, integer is represented as a 16-bit binary number. When the bits are rotated right, the rightmost bit rotates to the leftmost bit.

In Bin number base mode: rotR 0000111100001111 b 1000011110000111Ü

rotR 0000111100001111Ü = 1000011110000111Ü

rotR is not valid in Dec number base mode. To enter hexadecimal numbers Õ through Ú, use the BASE A-F menu. Do not use 1 to type a letter.

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round( MATH NUM menu

round(number,#ofDecimals) round(number)

Returns a real or complex number rounded to the specified #ofDecimals (0 to 11). If #ofDecimals is omitted, number is rounded to 12 decimal places. round(list,#ofDecimals) round(matrix,#ofDecimals) round(vector,#ofDecimals)

Returns a list, matrix, or vector in which each element is the rounded value of the corresponding element in the argument. #ofDecimals is optional.

rref MATRX OPS menu

rSwap( MATRX OPS menu

rref matrix

Returns the reduced row-echelon form of a real or complex matrix. The number of columns must be greater than or equal to the number of rows. rSwap(matrix,rowA,rowB)

Returns a matrix with rowA of a real or complex matrix swapped with rowB.

round(p,4) b round(p/4,4) b round(p/4) b

3.1416 .7854 .785398163397

round({p,‡2,ln 2},3) b {3.142 1.414 .693} round([[ln 5,ln 3][p,e^1]],2) [[1.61 1.1 ] b [3.14 2.72]]

[[4,5,6][7,8,9]]¶MAT b [[4 5 6] [7 8 9]] rref MAT b [[1 0 L.999999999999… [0 1 2 … [[5,3,1][2,0,4][3,L1,2]]¶MAT [[5 3 b [2 0 [3 L1 rSwap(MAT,2,3) b [[5 3 [3 L1 [2 0

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Chapter 20: A to Z Function and Instruction Reference

Scatter † STAT DRAW menu (Scatte shows on menu)

Scatter xList,yList

Draws a scatter plot on the current graph, using the real data pairs in xList and yList. Scatter

349

{L9,L6,L4,L1,2,5,7,10}¶XL b {L9 L6 L4 L1 2 5 7 1… {L7,L6,L2,1,3,6,7,9}¶YL b {L7 L6 L2 1 3 6 7 9} ZStd:Scatter XL,YL b

Uses the data in built-in variables xStat and yStat. These variables must contain valid data of the same dimension; otherwise, an error occurs.

Sci † mode screen

Sci

In Sci notation mode:

Sets scientific notation display mode.

123456789 b

1.23456789E8

In Normal notation mode: 123456789 b

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Chapter 20: A to Z Function and Instruction Reference

Select( LIST OPS menu

Select(xListName,yListName)

If a scatter plot or xyline plot is currently selected and plotted on the graph screen, you can select a subset (range) of those data points. The selected data points are stored to xListName and yListName. Select(xListName,yListName) displays the current

{L9,L6,L4,L1,2,5,7,10}¶L1 b {L9 L6 L4 L1 2 5 7 1… {L7,L6,L2,1,3,6,7,9}¶L2 b {L7 L6 L2 1 3 6 7 9} Plot1(1,L1,L2):ZStd b After the graph is displayed: Select(L10,L20) b

graph screen and starts an interactive session during which you select a range of data points. a. Move the cursor to the leftmost (left bound) point of the range you want to select and press b. b. Then move the cursor to the rightmost (right bound) point of the range you want to select and press b.

Move the cursor to point (2,3) and press b. Then move to (10,9) and press b.

A new stat plot of xListName and yListName replaces the plot from which you selected the points.

L10 b L20 b

Send( ‡ program editor I/O menu

Send(listName)

{2 5 7 10} {3 6 7 9}

{1,2,3,4,5}¶L1:Send(L1) b

Sends the contents of listName to the CBL or CBR System.

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Chapter 20: A to Z Function and Instruction Reference

seq(

seq(expression,variable,begin,end,step)

seq(expression,variable,begin,end)

Uses a step of 1.

SeqG † graph format screen

SetLEdit LIST OPS menu (SetLE shows on menu)

seq(x 2,x,1,8,2) b {1 9 25 49}

Returns a list containing a sequence of numbers created by evaluating expression from variable = begin to variable = end in increments of step.

MATH MISC menu

351

seq(x 2,x,1,8) b {1 4 9 16 25 36 49 6…

SeqG

Sets sequential graphing format, in which selected functions are plotted one at a time. SetLEdit column1ListName[, ... ,column20ListName]

Removes all lists from the list editor and then stores one or more ListNames in the specified order, starting with column 1.

{1,2,3,4}¶L1 b {5,6,7,8}¶L2 b SetLEdit L1,L2 b The list editor now contains:

SetLEdit

Removes all lists from the list editor and stores built-in lists xStat, yStat, and fStat in columns 1 through 3, respectively.

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Chapter 20: A to Z Function and Instruction Reference

Shade( GRAPH DRAW menu

Shade(lowerFunc,upperFunc,xLeft,xRight,pattern,patternRes)

Draws lowerFunc and upperFunc in terms of x on the current graph and shades the area bounded by lowerFunc, upperFunc, xLeft, and xRight. The shading style is determined by pattern (1 through 4) and patternRes (1 through 8).

In Func graphing mode: Shade(xN2,x^3N8 x,L5,1,2,3) b

pattern: 1 = vertical (default) 2 = horizontal

3 = negative-slope 45¡ 4 = positive-slope 45¡

ClDrw:Shade(x^3N8 x,xN2) b

patternRes (resolution): 1 = every pixel (default) 2 = every 2nd pixel 3 = every 3rd pixel 4 = every 4th pixel

5 = every 5th pixel 6 = every 6th pixel 7 = every 7th pixel 8 = every 8th pixel

Shade(lowerFunc,upperFunc)

Sets xLeft and xRight to xMin and xMax, respectively, and uses the defaults for pattern and patternRes.

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Chapter 20: A to Z Function and Instruction Reference

shftL BASE BIT menu

shftL integer

353

In Bin number base mode:

Returns a real integer with bits shifted one to the left. Internally, integer is represented as a 16-bit binary number. When the bits are shifted left, the leftmost bit is dropped and 0 is used as the rightmost bit.

shftL 0000111100001111 b 1111000011110Ü Leading zeros are not displayed.

shftL 0000111100001111Ü = 0001111000011110Ü

0 shftL is not valid in Dec number base mode. To enter hexadecimal numbers Õ through Ú, use the BASE A-F menu. Do not use 1 to type a letter.

shftR BASE BIT menu

shftR integer

Returns a real integer with bits shifted one to the right. Internally, integer is represented as a 16-bit binary number. When the bits are shifted right, the rightmost bit is dropped and 0 is used as the leftmost bit.

In Bin number base mode: shftR 0000111100001111 b 11110000111Ü Leading zeros are not displayed.

shftR 0000111100001111Ü = 0000011110000111Ü

0 shftR is not valid in Dec number base mode. To enter hexadecimal numbers Õ through Ú, use the BASE A-F

menu. Do not use 1 to type a letter.

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Chapter 20: A to Z Function and Instruction Reference

ShwSt CATALOG

sign MATH NUM menu

ShwSt

Displays the results of the most recent stat calculation. sign number or sign (expression)

Returns L1 if the argument is < 0, 1 if it is > 0, or 0 if it is = 0. The argument must be real. sign list

Returns a list in which each element is L1, 1, or 0 to indicate the sign of the corresponding element in list.

SimulG † graph format screen

simult( †-u

sign L3.2 b sign (6+2N8) b

L1 0

sign {L3.2,16.8,6+2N8} b {L1 1 0}

SimulG

Sets simultaneous graphing format, in which all selected functions are plotted at the same time. simult(squareMatrix,vector)

Solve the following for x and y:

Returns a vector containing the solutions to a system of simultaneous linear equations that have the form: a 1,1x 1 + a 1,2x2 + a1,3x3 + ... = b1 a 2,1x 1 + a 2,2x2 + a2,3x3 + ... = b2 a 3,1x 1 + a 3,2x2 + a3,3x3 + ... = b3

3x N 4y = 7 x + 6y = 6

Each row in squareMatrix contains the a coefficients of an equation, and vector contains the b constants.

simult(MAT,VEC) b

[[3,L4][1,6]]¶MAT b [7,6]¶VEC b

The solution is x=3 and y=.5.

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Chapter 20: A to Z Function and Instruction Reference

sin =

sin angle or sin (expression)

sin p/2 b sin (p/2) b sin 45¡ b

An angle is interpreted as degrees or radians according to the current angle mode. In any angle mode, you can designate an angle as degrees or radians by using the ¡ or r designator, respectively, from the MATH ANGLE menu.

sin 45 b sin (p/2) r b

Returns a list in which each element is the sine of the corresponding element in list. sin squareMatrix The squareMatrix cannot have repeated eigenvalues.

sin L1 -{

In Radian angle mode:

Returns the sine of angle or expression, which can be real or complex.

sin list

355

0 1 .707106781187

In Degree angle mode: .707106781187 1

In Radian angle mode: sin {0,p/2,p} b

{0 1 0}

In Degree angle mode: sin {0,30,90} b

{0 .5 1}

Returns a square matrix that is the matrix sine of squareMatrix. The matrix sine corresponds to the result calculated using power series or Cayley-Hamilton Theorem techniques. This is not the same as simply calculating the sine of each element. sin L1 number or sin L1 (expression)

Returns the arcsine of number or expression, which can be real or complex. sin L1 list

Returns a list in which each element is the arcsine of the corresponding element in list.

In Radian angle mode: sinL1 .5 b sin L1 {0,.5} b

.523598775598 {0 .523598775598}

In Degree angle mode: sinL1 1 b

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Chapter 20: A to Z Function and Instruction Reference

sinh MATH HYP menu

sinh number or sinh (expression)

sinh list

Returns a list in which each element is the hyperbolic sine of the corresponding element in list.

sinhL1 MATH HYP menu

sinh 1.2 b

1.50946135541

Returns the hyperbolic sine of number or expression, which can be real or complex.

sinh L1 number or sinh L1(expression)

sinh {0,1.2} b {0 1.50946135541}

sinhL1 1 b

.88137358702

Returns the inverse hyperbolic sine of number or expression, which can be real or complex. sinh L1 list

Returns a list in which each element is the inverse hyperbolic sine of the corresponding element in list.

sinhL1 {1,2.1,3} b {.88137358702 1.4874…

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Chapter 20: A to Z Function and Instruction Reference

SinR STAT CALC menu Built-in equation variables such as y1, r1, and xt1 are case-sensitive. Do not use Y1, R1, and XT1.

If you specify a period, the TI-86 may find a solution more quickly or it may find a solution when one would not have been found otherwise.

SinR [iterations,] xList,yList [,period],equationVariable

Attempts to fit a sinusoidal regression model (y=a sin(bx+c)+d) to real data pairs in xList and yList, using an optional estimated period. The regression equation is stored to equationVariable, which must be a built-in equation variable such as y1, r1, and xt1. The equation’s coefficients always are stored as a list to built-in variable PRegC. iterations is optional; it specifies the maximum number of times (1 through 16) the TI-86 will attempt to find a solution. If omitted, 8 is used. Typically, larger values result in better accuracy but longer execution times, and vice versa.

357

seq(x,x,1,361,30)¶L1 b {1 31 61 91 121 151 … {5.5,8,11,13.5,16.5,19,19.5,17, 14.5,12.5,8.5,6.5,5.5}¶L2 b {5.5 8 11 13.5 16.5… SinR L1,L2,y1 b

Plot1(1,L1,L2) b ZData b

If you omit the optional period, the difference between values in xList should be equal and in sequential order. If you specify period, the differences between x values can be unequal. Values used for xList and yList are stored automatically to built-in variables xStat and yStat, respectively. The regression equation is stored also to built-in equation variable RegEq. The output of SinR is always in radians, regardless of the angle mode setting. SinR [iterations,] xList,yList [,period]

Stores the regression equation to RegEq only.

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Chapter 20: A to Z Function and Instruction Reference SinR [iterations,] equationVariable

Uses xStat and yStat for xList and yList, respectively. These built-in variables must contain valid data of the same dimension; otherwise, an error occurs. The regression equation is stored to equationVariable and RegEq. SinR [iterations]

Uses xStat and yStat, and stores the regression equation to RegEq only.

SlpFld † graph format screen (scroll down to second screen)

Solver( †-t

SlpFld

In DifEq graphing mode, turns on slope fields. To turn off direction and slope fields, use FldOff. Solver(equation,variable,guess,{lower,upper})

Solves equation for variable, given an initial guess and lower and upper bounds within which the solution is sought. equation can be an expression, which is assumed to equal 0.

If y=5, solve x 3+y 2=125 for x. You guess the solution is approximately 4: 5¶y b 5 Done Solver(x^3+y 2=125,x,4) b x b 4.64158883361

Solver(equation,variable,guess)

Uses L1E99 and 1E99 for upper and lower, respectively. Solver(equation,variable,{guessLower,guessUpper})

Uses the secant line between guessLower and guessUpper to start the search. Solver( will still search for a solution outside of this range.

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Chapter 20: A to Z Function and Instruction Reference

sortA

SortA list

Returns a list in which the real or complex elements of list are sorted in ascending order.

LIST OPS menu

sortD

SortD list

Returns a list in which the real or complex elements of list are sorted in descending order.

LIST OPS menu

Sortx LIST OPS menu

Sortx xListName,yListName,frequencyListName Sortx xListName,yListName

In ascending order of x elements, sorts real or complex x and y data pairs and, optionally, their frequencies in

359

{5,8,L4,0,L6}¶L1 b SortA L1 b

{5 8 L4 0 L6} {L6 L4 0 5 8}

{5,8,L4,0,L6}¶L1 b SortD L1 b

{5 8 L4 0 L6} {8 5 0 L4 L6}

{3,1,2}¶XL b {0,8,L4}¶YL b Sortx XL,YL b XL b YL b

{3 1 2} {0 8 L4} Done {1 2 3} {8 L4 0}

{3,1,2}¶XL b {0,8,L4}¶YL b Sorty XL,YL b YL b XL b

{3 1 2} {0 8 L4} Done {L4 0 8} {2 3 1}

xListName, yListName, and frequencyListName. The lists’ contents are updated to reflect the changes. Sortx

Uses built-in variables xStat and yStat for xListName and yListName, respectively. These built-in variables must contain valid data of the same dimension; otherwise, an error occurs.

Sorty LIST OPS menu

Sorty xListName,yListName,frequencyListName Sorty xListName,yListName

In ascending order of y elements, sorts real or complex x and y data pairs and, optionally, their frequencies in xListName, yListName, and frequencyListName. The lists’ contents are updated to reflect the changes.

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Chapter 20: A to Z Function and Instruction Reference Sorty

Uses built-in variables xStat and yStat for xListName and yListName, respectively. These built-in variables must contain valid data of the same dimension; otherwise, an error occurs.

4Sph

vector 4Sph

VECTR OPS menu

SphereV †-m

Square:

2

I

Displays a 2- or 3-element vector as spherical coordinates in [r q 0] or [r q f] form, respectively, even if the display mode is not set for spherical (SphereV). SphereV

Sets spherical vector coordinate mode [r q f]. number 2 or (expression)2 list 2 squareMatrix2 Returns a real or complex argument multiplied by itself. To square a negative number, enclose it in parentheses. A squareMatrix multiplied by itself is not the same as simply squaring each element.

Square root: ‡ -ˆ

‡number or ‡(expression)

Returns the square root of number or expression, which can be real or complex.

In RectV vector coordinate mode: [0,L1]4Sph b [1±L1.57079632679±1.… [0,0,L1]4Sph b [1±0±3.14159265359] In SphereV vector coordinate mode: [1,2] b [2.2360679775±1.1071… 25 2 b (16+9)2 b

L2 2 b (L2) 2 b

L4 4

{L2,4,25} b 2

[[2,3][4,5]] b 2

‡25 b ‡(25+11) b

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625 625

{4 16 625} [[16 21] [28 37]] 5 6

Chapter 20: A to Z Function and Instruction Reference ‡list

In RectC complex number mode:

Returns a list in which element is the square root of the corresponding element in list.

St4Eq( STRNG menu

St4Eq(stringVariable,equationVariable)

Converts stringVariable to a number, expression, or equation, and stores it in equationVariable. To convert the string and retain the same variable name, you can set equationVariable equal to stringVariable. If you use Input instead of InpSt here, the entered expression is evaluated at the current value of x and the result (not the expression) is stored.

StGDB † GRAPH menu

361

‡{L2,25} b {(0,1.41421356237) (… "5"¶x:6 x b ERROR 10 DATA TYPE "5"¶x:St4Eq(x,x):6 x b 30 Program segment: © :InpSt "Enter y1(x):",STR :St4Eq(STR,y1) :Input "Enter x:",x :Disp "Result is:",y1(x) © You cannot store a string directly to a built-in equation variable.

StGDB graphDataBaseName

Creates a graph database (GDB) variable that contains the current: • Graphing mode, graph format settings, and range variables. • Functions in the equation editor, whether they are selected, and their graph styles. To restore the database and recreate the graph, use RcGDB (page 343).

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Chapter 20: A to Z Function and Instruction Reference

Stop ‡ program editor CTL menu

Stop

Program segment:

Ends program execution and returns to the home screen. Use N==999, not N=999.

Store to variable: ¶ X

number ¶ variable or (expression) ¶ variable string ¶ variable list ¶ variable vector ¶ variable matrix ¶ variable Stores the specified argument to variable.

StPic † GRAPH menu

StReg( STAT CALC menu

© :Input N :If N==999 :Stop © 10¶A:4¹A b "Hello"¶STR b

40 Hello

{1,2,3}¶L1 b

{1 2 3}

[1,2,3]¶VEC b

[1 2 3]

[[1,2,3][4,5,6]]¶MAT b [[1 2 3] [4 5 6]]

StPic pictureName

Stores a picture of the current graph screen to pictureName. {1,2,3,4,5}¶L1 b

StReg(variable)

Stores the most recently calculated regression equation to variable. This lets you save a regression equation by storing it to any variable as opposed to a built-in equation variable. - – EQ b recalls the equation. Then b evaluates it at the current value of x.

{1 2 3 4 5} {1,20,55,230,742}¶L2 b {1 20 55 230 742} ExpR L1,L2:StReg(EQ) b Done 8¶x b 8 Rcl EQ b .41138948780597¹4.7879605684671^x 113620.765451 b

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Chapter 20: A to Z Function and Instruction Reference

String entry: " STRNG menu ‡ program editor I/O menu

sub( STRNG menu

Subtraction: N T

"string"

Defines a string. When you display a string, it is leftjustified on the screen. Strings are interpreted as text characters, not numbers. For example, you cannot perform a calculation with strings such as "4" or "A¹8". To convert between string variables and equation variables, use Eq4St( and St4Eq( as described on pages 290 and 361, respectively. sub(string,begin,length)

Returns a new string that is a subset of string, starting at character number begin and continuing for the specified length. numberA N numberB Returns the value of numberB subtracted from numberA. The arguments can be real or complex. list N number Returns a list in which number is subtracted from each element of list. The arguments can be real or complex.

363

"Hello"¶STR b Hello Disp STR+", Jan" b Hello, Jan Done

"The answer is:"¶STR b The answer is: sub(STR,5,6) b answer

6N2 b 10NL4.5 b {10,9,8}N4 b

4 14.5 {6 5 4}

In RectC complex number mode: {8,1,(5,2)}N3 b {(5,0) (L2,0) (2,2)}

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Chapter 20: A to Z Function and Instruction Reference listA N listB matrixA N matrixB vectorA N vectorB Returns a list, matrix, or vector that is the result of each element in the second argument subtracted from the corresponding element in the first argument. The two real or complex arguments must have the same dimension.

sum MATH MISC menu

sum list

Returns the sum of all real or complex elements in list.

{5,7,9}N{4,5,6} b

{1 2 3}

[[5,7,9][11,13,15]]N[[4,5,6][7,8, 9]] b [[1 2 3] [4 5 6]] [5,7,9]N[1,2,3] b

[4 5 6]

sum {1,2,4,8} b

15

sum {2,7,L8,0} b

1

LIST OPS menu

tan ?

tan angle or tan (expression)

In Radian angle mode:

Returns the tangent of angle or expression, which can be real or complex.

tan p/4 b tan (p/4) b tan 45¡ b

An angle is interpreted as degrees or radians according to the current angle mode. In any angle mode, you can designate an angle as degrees or radians by using the ¡ or r designator, respectively, from the MATH ANGLE menu.

tan 45 b tan (p/4) r b

tan list

Returns a list in which each element is the tangent of the corresponding element in list.

0 1 1

In Degree angle mode: 1 1

In Degree angle mode: tan {0,45,60} b {0 1 1.73205080757}

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Chapter 20: A to Z Function and Instruction Reference

tan L1 -}

tanL1 number or tanL1 (expression)

Returns the arctangent of number or expression, which can be real or complex.

In Radian angle mode: tanL1 .5 b

.463647609001

In Degree angle mode: tanL1 1 b

tanL1 list

Returns a list in which each element is the arctangent of the corresponding element in list.

tanh MATH HYP menu

tanh number or tanh (expression)

Returns a list in which each element is the hyperbolic tangent of the corresponding element in list.

MATH HYP menu

45

In Radian angle mode: tanL1 {0,.2,.5} b {0 .19739555985 .463… tanh 1.2 b

.833654607012

Returns the hyperbolic tangent of number or expression, which can be real or complex. tanh list

tanh L1

365

tanh L1 number or tanh L1(expression)

tanh {0,1.2} b {0 .833654607012}

tanhL1 0 b

0

Returns the inverse hyperbolic tangent of number or expression, which can be real or complex. tanh L1 list

Returns a list in which each element is the inverse hyperbolic tangent of the corresponding element in list.

In RectC complex number mode: tanhL1 {0,2.1} b {(0,0) (.51804596584…

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TanLn( GRAPH DRAW menu

Text( † GRAPH DRAW menu

TanLn(expression,xValue)

Draws expression on the current graph and then draws a tangent line at xValue.

Text(row,column,string)

Writes a text string on the current graph beginning at pixel (row,column), where 0  row  57 and 0  column  123. Text at the bottom of the graph may be covered by a displayed menu. To remove the menu, press :.

Then ‡ program editor CTL menu

In Func graphing mode and Radian angle mode: ZTrig:TanLn(cos x,p/4) b

Program segment in Func graphing mode and a ZStd graph screen: © :y1=x sin x :Text(0,70,"y1=x sin x") © When executed:

Refer to syntax information for If, beginning on page 305. See the If:Then:End and If:Then:Else:End syntax.

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Chapter 20: A to Z Function and Instruction Reference

Trace

Trace

† GRAPH menu

Transpose:

367

T

MATRX MATH menu

Displays the current graph and lets the user trace a function. From a program, press b to stop tracing and continue with the program. [[1,2][3,4]]¶MATA b

matrixT Returns a transposed real or complex matrix in which element row,column is swapped with element column,row of matrix. For example: a b

ã c dä

T

returns

a c

ã b dä

For complex matrices, the complex conjugate of each element is taken.

[[1 2] [3 4]] MATAT b

[[1 3] [2 4]]

[[1,2,3][4,5,6][7,8,9]]¶MATB [[1 2 3] b [4 5 6] [7 8 9]] MATBT b

[[1 4 7] [2 5 8] [3 6 9]]

In RectC complex number mode: [[(1,2),(1,1)][(3,2),(4,3)]] ¶MATC b [[(1,2) (1,1)] [(3,2) (4,3)]] MATCT b

20ATOZ.DOC TI-86, Chap 20, US English Bob Fedorisko Revised: 02/13/01 2:42 PM Printed: 02/13/01 3:05 PM Page 367 of 118

[[(1,L2) (3,L2)] [(1,L1) (4,L3)]]

368

Chapter 20: A to Z Function and Instruction Reference

TwoVar STAT CALC menu (TwoVa shows on menu)

TwoVar xList,yList,frequencyList

Performs two-variable statistical analysis on the real data pairs in xList and yList, using the frequencies in frequencyList.

{0,1,2,3,4,5,6}¶L1 b {0 1 2 3 4 5 6} {0,1,2,3,4,5,6}¶L2 b {0 1 2 3 4 5 6} TwoVar L1,L2 b

Values used for xList, yList, and frequencyList are stored automatically to the built-in variables xStat, yStat, and fStat, respectively. TwoVar xList,yList

Uses frequencies of 1.

Scroll down to see more results.

TwoVar

Uses xStat, yStat, and fStat for xList, yList, and frequencyList. These built-in variables must contain valid data of the same dimension; otherwise, an error occurs.

unitV VECTR MATH menu

unitV vector

In RectV vector coordinate mode:

Returns a unit vector of a real or complex vector, where: unitV [a,b,c] returns [

unitV [1,2,1] b [.408248290464 .8164…

a b c ] norm norm norm

and norm is

(a2+b2+c2).

20ATOZ.DOC TI-86, Chap 20, US English Bob Fedorisko Revised: 02/13/01 2:42 PM Printed: 02/13/01 3:05 PM Page 368 of 118

Chapter 20: A to Z Function and Instruction Reference

vc4li LIST OPS menu

vc4li vector

Returns a real or complex vector converted to a list.

VECTR OPS menu

Vector entry: [ ] - „ and - …

Vert † GRAPH DRAW menu

While ‡ program editor CTL menu

[element1,element2, ... ]

Defines a vector in which each element is a real or complex number or variable. Vert xValue

Draws a vertical line on the current graph at xValue.

:While condition :commands-while-true :End :command

Executes commands-while-true as long as condition is true.

vc4li [2,7,L8,0] b

369

{2 7 L8 0}

(vc4li [2,7,L8,0]) 2 b {4 49 64 0} [4,5,6]¶VEC b

[4 5 6]

In PolarC complex number mode: [5,(2±p/4)]¶VEC b [(5±0) (2±.785398163… In a ZStd graph screen: Vert L4.5 b

Program segment: © :1¶J :0¶TEMP :While J20 : TEMP+1/J¶TEMP : J+1¶J :End :Disp "Reciprocal sums to 20",TEMP ©

20ATOZ.DOC TI-86, Chap 20, US English Bob Fedorisko Revised: 02/13/01 2:42 PM Printed: 02/13/01 3:05 PM Page 369 of 118

370

Chapter 20: A to Z Function and Instruction Reference

xor BASE BOOL menu

integerA xor integerB Compares two real integers bit by bit. Internally, both integers are converted to binary. When corresponding bits are compared, the result is 1 if either bit (but not both) is 1; the result is 0 if both bits are 0 or both bits are 1. The returned value is the sum of the bit results. For example, 78 xor 23 = 89.

In Dec number base mode: 78 xor 23 b

89

In Bin number base mode: 1001110 xor 10111 b Ans4Dec b

1011001Ü 89Þ

78 = 1001110Ü 23 = 0010111Ü 1011001Ü = 89 You can enter real numbers instead of integers, but they are truncated automatically before the comparison.

xyline † STAT DRAW menu

xyline xList,yList

Draws a line plot on the current graph, using the real data pairs in xList and yList. xyline

{L9,L6,L4,L1,2,5,7,10}¶XL b {L9 L6 L4 L1 2 5 7 1… {L7,L6,L2,1,3,6,7,9}¶YL b {L7 L6 L2 1 3 6 7 9} ZStd:xyline XL,YL b

Uses the data in built-in variables xStat and yStat. These variables must contain valid data of the same dimension; otherwise, an error occurs.

20ATOZ.DOC TI-86, Chap 20, US English Bob Fedorisko Revised: 02/13/01 2:42 PM Printed: 02/13/01 3:05 PM Page 370 of 118

Chapter 20: A to Z Function and Instruction Reference

ZData † GRAPH ZOOM menu

ZData

Adjusts the window variable values based on the currently defined statistical plots so that all stat data points will be plotted, and then updates the graph screen.

371

In Func graphing mode: {1,2,3,4}¶XL b {2,3,4,5}¶YL b Plot1(1,XL,YL) b ZStd b

ZData b

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{1 2 3 4} {2 3 4 5} Done

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Chapter 20: A to Z Function and Instruction Reference

ZDecm † GRAPH ZOOM menu

ZDecm

In Func graphing mode:

Sets the window variable values such that @[email protected]=.1, and then updates the graph screen with the origin centered on the screen. xMin=L6.3 xMax=6.3 xScl=1

y1=x sin x b ZStd b

Done

yMin=L3.1 yMax=3.1 yScl=1

One of the benefits of ZDecm is that you can trace in .1 increments.

If you trace the graph above, x values start at 0 and increment by .1587301587. ZDecm b

If you trace this graph, the x values increment by .1.

20ATOZ.DOC TI-86, Chap 20, US English Bob Fedorisko Revised: 02/13/01 2:42 PM Printed: 02/13/01 3:05 PM Page 372 of 118

Chapter 20: A to Z Function and Instruction Reference

ZFit

ZFit

In Func graphing mode:

Recalculates yMin and yMax to include the minimum and maximum y values of the selected functions between the current xMin and xMax, and then updates the graph screen.

† GRAPH ZOOM menu

373

y1=x 2N20 b ZStd b

Done

This does not affect xMin and xMax. ZFit b

ZIn † GRAPH ZOOM menu

ZIn

In Func graphing mode:

Zooms in on the part of the graph centered around the current cursor location.

y1=x sin x b ZStd b

Zoom factors are set by the values of built-in variables xFact and yFact; the default is 4 for both factors.

ZIn b

20ATOZ.DOC TI-86, Chap 20, US English Bob Fedorisko Revised: 02/13/01 2:42 PM Printed: 02/13/01 3:05 PM Page 373 of 118

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374

Chapter 20: A to Z Function and Instruction Reference

ZInt † GRAPH ZOOM menu

ZInt

In Func graphing mode:

Sets the window variable values so that each pixel is an integer in all directions (@[email protected]=1), sets xScl=yScl=10, and then updates the graph screen.

y1=der1(x 2N20,x) b ZStd b

Done

The current cursor location becomes the center of the new graph. One of the benefits of ZInt is that you can trace in whole number increments.

If you trace the graph above, x values start at 0 and increment by .1587301587. ZInt b

If you trace this graph, x values increment by 1.

20ATOZ.DOC TI-86, Chap 20, US English Bob Fedorisko Revised: 02/13/01 2:42 PM Printed: 02/13/01 3:05 PM Page 374 of 118

Chapter 20: A to Z Function and Instruction Reference

ZOut † GRAPH ZOOM menu

ZOut

In Func graphing mode:

Zooms out to display more of the graph, centered around the current cursor location.

y1=x sin x b ZStd b

Zoom factors are set by the values of built-in variables xFact and yFact; the default is 4 for both factors.

ZOut b

ZPrev † GRAPH ZOOM menu

375

ZPrev

Replots the graph using the window variable values of the graph that was displayed before you executed the previous ZOOM instruction.

20ATOZ.DOC TI-86, Chap 20, US English Bob Fedorisko Revised: 02/13/01 2:42 PM Printed: 02/13/01 3:05 PM Page 375 of 118

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376

Chapter 20: A to Z Function and Instruction Reference

ZRcl

ZRcl

Sets the window variables to values stored previously in the user-defined zoom-window variables, and then updates the graph screen.

† GRAPH ZOOM menu

To set user-defined zoom-window variables, either: • Press 6 ( / / / & (ZSTO) to store the current graph’s window variables. – or – • Store the applicable values to the zoom-window variables, whose names begin with z followed by the regular window variable name. For example, store a value for xMin to zxMin, yMin to zyMin, etc.

ZSqr † GRAPH ZOOM menu

ZSqr

In Func graphing mode:

Sets the window variable values to produce “square” pixels where @[email protected], and then updates the graph screen.

y1=‡(8 2Nx 2):y2=Ly1 b ZStd b

The center of the current graph (not necessarily the axes intersection) becomes the center of the new graph. In other types of zooms, squares may look like rectangles and circles may look like ovals. Use ZSqr for a more accurate shape.

ZSqr b

20ATOZ.DOC TI-86, Chap 20, US English Bob Fedorisko Revised: 02/13/01 2:42 PM Printed: 02/13/01 3:05 PM Page 376 of 118

Done

Chapter 20: A to Z Function and Instruction Reference

ZStd † GRAPH ZOOM menu

ZStd

377

In Func graphing mode:

Sets the window variables to the standard default values, and then updates the graph screen.

y1=x sin x b ZStd b

Func graphing mode: xMin=L10 xMax=10 xScl=1

yMin=L10 yMax=10 yScl=1

Pol graphing mode: qMin=0 xMin=L10 yMin=L10 qMax=6.28318530718 (2p) xMax=10 yMax=10 qStep=.130899693899… (p/24) xScl=1 yScl=1 Param graphing mode: tMin=0 xMin=L10 yMin=L10 tMax=6.28318530718 (2p) xMax=10 yMax=10 tStep=.130899693899… (p/24) xScl=1 yScl=1 DifEq graphing mode: tMin=0 xMin=L10 yMin=L10 tMax=6.28318530718 (2p) xMax=10 yMax=10 tStep=.130899693899… (p/24) xScl=1 yScl=1 tPlot=0 difTol=.001

20ATOZ.DOC TI-86, Chap 20, US English Bob Fedorisko Revised: 02/13/01 2:42 PM Printed: 02/13/01 3:05 PM Page 377 of 118

Done

378

Chapter 20: A to Z Function and Instruction Reference

ZTrig † GRAPH ZOOM menu

ZTrig

In Func graphing mode:

Sets the window variables to preset values appropriate for plotting trig functions in Radian angle mode (@x=p/24), and then updates the graph screen. xMin=L8.24668071567 xMax=8.24668071567 xScl=1.5707963267949 (p/2)

y1=sin x b ZStd b

yMin=L4 yMax=4 yScl=1 ZTrig b

20ATOZ.DOC TI-86, Chap 20, US English Bob Fedorisko Revised: 02/13/01 2:42 PM Printed: 02/13/01 3:05 PM Page 378 of 118

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379

Appendix

A

Appendix TI-86

TI-86 Menu Map.............................................................. 380 Handling a Difficulty ........................................................ 392 Error Conditions............................................................... 393 Equation Operating System (EOSé) ................................ 397 TOL (The Tolerance Editor) - ™ )................... 398 Computational Accuracy.................................................. 399 Support and Service Information ..................................... 400 Warranty Information ...................................................... 402 M1

M2

M3

M4

M5

F1

F2

F3

F4

F5

99APPX.DOC TI-86, Appendix, US English Bob Fedorisko Revised: 02/27/01 1:20 PM Printed: 02/27/01 1:26 PM Page 379 of 26

380

Appendix

TI-86 Menu Map This section presents the TI-86 menus as they appear on the TI-86 keyboard, starting at the top. If a menu has items that display other menus, the other menus follow directly below the main menu. In the program editor, the appearance of some menus changes slightly. The menu map omits user-created-name menus, such as the LIST NAMES and CONS USER menus. -o

LINK Menu The link menus are not available in the program editor.

SEND

RECV SND85

LINK SEND Menu

-o&

BCKUP PRGM MATRX GDB

SEND BCKUP Menu

ALL

4

4

CONS

MATH DRAW FORMT STGDB RCGDB 4

EVAL

LIST

VECTR REAL

CPLX

EQU

PIC

WIND STRNG

-o&&

XMIT

LINK SEND Selection Screen Menu XMIT

SELCT ALL+

LINK SND85 Menu MATRX

In the program editor, DrEqu is available as a GRAPH menu item.

LIST

y(x)=

WIND

-o(

VECTR REAL

GRAPH Menu

- o & data type

ALLN

CPLX

4

CONS

PIC

STRNG

6 in Func graphing mode ZOOM TRACE GRAPH 4

99APPX.DOC TI-86, Appendix, US English Bob Fedorisko Revised: 02/27/01 1:20 PM Printed: 02/27/01 1:26 PM Page 380 of 26

STPIC RCPIC

Appendix GRAPH Menu r(q)=

WIND

GRAPH Menu E(t)=

WIND

GRAPH Menu Q'(t)=

WIND

6 in Pol graphing mode ZOOM TRACE GRAPH 4

WIND y

WIND r

WIND xt

MATH DRAW FORMT STGDB RCGDB 4

AXES GRAPH 4 FORMT DRAW ZOOM TRACE EXPLR 4

STPIC RCPIC

EVAL

STPIC RCPIC

EVAL STGDB RCGDB STPIC RCPIC

6 & in Func graphing mode

ZOOM TRACE GRAPH INSf DELf SELCT 4

ALL+

ALLN STYLE

6 & in Pol graphing mode

ZOOM TRACE GRAPH INSf DELf SELCT 4

Equation Editor Menu E(t)= t

EVAL

6 in DifEq graphing mode INITC

Equation Editor Menu r(q)= q

MATH DRAW FORMT STGDB RCGDB 4

6 in Param graphing mode ZOOM TRACE GRAPH 4

Equation Editor Menu y(x)= x

ALL+

ALLN STYLE

6 & in Param graphing mode

ZOOM TRACE GRAPH yt DELf SELCT 4

INSf

ALL+

ALLN STYLE

Equation Editor Menu 6 & in DifEq graphing mode Q'(t)= t

WIND Q

381

INITC INSf

AXES GRAPH DELf SELCT 4

ALL+

ALLN STYLE

99APPX.DOC TI-86, Appendix, US English Bob Fedorisko Revised: 02/27/01 1:20 PM Printed: 02/27/01 1:26 PM Page 381 of 26

382

Appendix GRAPH VARS (Graph Variables) Menu y(x)= y

WIND x

ZOOM TRACE GRAPH xt yt t 4

r

GRAPH WIND (Window Variables) Menu y(x)= xMin

WIND xMax

ZOOM TRACE GRAPH xScl yMin yMax 4

GRAPH ZOOM Menu To display the GRAPH ZOOM menu in DifEq mode, press 6 / (.

y(x)= BOX

WIND ZIN

yScl

6 & in the program editor only q

Q1

Q'1

t

4

FnOn

4

fldRes

tMin

tMax

tStep

qMin

4

qMax

4

EStep

ZFIT

ZSQR ZTRIG ZDECM ZDATA 4

dTime

qStep

tPlot

difTol

xRes

ZRCL ZFACT ZOOMX ZOOMY ZINT ZSTO

6 / & in Func graphing mode

MATH DRAW FORMT STGDB RCGDB ROOT dyàdx ‰f(X) FMIN FMAX 4

GRAPH MATH Menu

Q[

6(

ZOOM TRACE GRAPH ZOUT ZSTD ZPREV 4

GRAPH MATH Menu

Axes

6 ' in the program editor only

4

DifEq graphing mode has no GRAPH MATH menu.

FnOff

INFLC YICPT ISECT

DIST

ARC

4 TANLN

6 / & in Pol graphing mode

MATH DRAW FORMT STGDB RCGDB DIST dyàdx dràdq ARC TANLN

99APPX.DOC TI-86, Appendix, US English Bob Fedorisko Revised: 02/27/01 1:20 PM Printed: 02/27/01 1:26 PM Page 382 of 26

Appendix

383

6 / & in Param graphing mode

GRAPH MATH Menu

MATH DRAW FORMT STGDB RCGDB DIST dyàdx dyàdt dxàdt ARC 4 TANLN

6/'

GRAPH DRAW Menu DrInv is available only in

Func graphing mode.

MATH DRAW FORMT STGDB RCGDB Shade LINE VERT HORIZ CIRCL 4

DrawF

PEN

PTON PTOFF PTCHG 4 CLDRW PxOn

DrEqu is available only in DifEq graphing mode.

4

SOLVER Menu - t equation b GRAPH WIND

TABLE Menu

ZOMM TRACE SOLVE

7

x

y

q

SIMULT ENTRY Menu NEXT

BOX

ZINT

ZOUT ZFACT ZSTD

7'

CLRq

in Param graphing mode TBLST SELCT

in Pol graphing mode

PREV

DrInv

TABLE

Table Screen Menu 7 & in Func graphing mode

TBLST SELCT

TanLn

SOLVER ZOOM Menu - t equation b (

TABLE SETUP Menu

TABLE TBLST

TBLST SELCT

TEXT

PxOff PxChg PxTest

t

xt

yt

in DifEq graphing mode

r

TBLST SELCT

- u (integer ‚ 2 &  30) b SOLVE

t

Q

SIMULT RESULT Menu COEFS STOa

99APPX.DOC TI-86, Appendix, US English Bob Fedorisko Revised: 02/27/01 1:20 PM Printed: 02/27/01 1:26 PM Page 383 of 26

STOb

*

STOx

384

Appendix 8

PRGM Menu NAMES EDIT

8 ' program name b

Program Editor Menu PAGE$ PAGE#

IàO

CTL

4

INSc

IàO Disp

CTL DispG

INSc DispT

IàO Else

CTL For

POLY ENTRY Menu

ClTbl

Get

Send

getKy ClLCD

INSc End

4

While

Repea

Menu

Lbl

- v (integer ‚ 2 &  30) b

CLRq

SOLVE

CUSTOM Menu Use the CUSTOM menu to create your own menu (Chapter 2).

4

Goto

Outpt

InpSt

4

IS>

DS<

Pause

4

DelVa

GrStl

LCust

Retur

Stop

STAT

WIND

*

COEFS STOa

9

CATLG-VARS Menu ALL

"

POLY RESULT Menu

4

CATLG

4

8 ' programName b )

PRGM CTL (Control) Menu PAGE$ PAGE# If Then

:

8 ' program name b (

PRGM IàO (InputàOutput) Menu PAGE$ PAGE# Input Promp

DELc UNDEL

REAL

4

-w CPLX

LIST

CATLG-VARS Selection Menu

4 VECTR MATRX STRNG

EQU

CONS

4

PRGM

- w & or select a data type

PAGE$ PAGE# CUSTM BLANK

99APPX.DOC TI-86, Appendix, US English Bob Fedorisko Revised: 02/27/01 1:20 PM Printed: 02/27/01 1:26 PM Page 384 of 26

GDB

PIC

Appendix CALC Menu evalF

nDer

MATRX Menu NAMES EDIT

-† der1

der2

fnInt

4

MATH norm

OPS

MATH ident

MATRX CPLX Menu NAMES EDIT conj real

VECTR Menu NAMES EDIT

MATH imag

INSr

VECTR MATH Menu NAMES EDIT cross unitV

MATH norm

arc

DELr

INSc

- ‰ ' matrixName b DELc

4REAL

-‰( OPS eigVl

CPLX eigVc

4

OPS ref

CPLX rref

rnorm cnorm

LU

cond

-‰) 4

aug

rSwap

rAdd

multR mRAdd 4

randM

-‰* OPS abs

CPLX angle

-Š MATH

fMax

Matrix Editor Menu

CPLX

MATRX OPS (Operations) Menu NAMES EDIT dim Fill

fMin

-‰ MATH

MATRX MATH Menu NAMES EDIT T det

385

OPS

Vector Editor Menu CPLX

INSi

DELi

- Š ' vectorName b

4REAL

-Š( OPS dot

CPLX

99APPX.DOC TI-86, Appendix, US English Bob Fedorisko Revised: 02/27/01 1:20 PM Printed: 02/27/01 1:26 PM Page 385 of 26

386

Appendix VECTR OPS (Operations) Menu

-Š)

NAMES EDIT dim Fill

4

MATH 4Pol

VECTR CPLX Menu NAMES EDIT conj real

MATH imag

OPS 4Cyl

CPLX 4Sph

real

MATH Menu NUM

imag

abs

-‹

angle

4

4Rec

MISC

4

INTER

PROB ANGLE iPart fPart

PROB ANGLE nPr nCr

MATH ANGLE Menu NUM

¡

4Pol



PROB ANGLE

HYP

HYP int

-Œ&

MISC abs

4

HYP rand

MISC randln

sign

min

max

mod

-Œ'

MATH PROB (Probability) Menu NUM !

vc4li

CPLX angle

MATH NUM (Number) Menu NUM round

li4vc

-Š* OPS abs

CPLX (Complex Number) Menu conj

4Rec

4

randN randBi

-Œ(

PROB ANGLE HYP r 4DMS

MISC

'

99APPX.DOC TI-86, Appendix, US English Bob Fedorisko Revised: 02/27/01 1:20 PM Printed: 02/27/01 1:26 PM Page 386 of 26

387

Appendix MATH HYP (Hyperbolic) Menu NUM sinh

PROB ANGLE HYP cosh tanh sinh L1

MISC cosh L1

-Œ) 4

tanh L1

-Œ*

MATH MISC (Miscellaneous) Menu NUM sum

PROB ANGLE prod seq

HYP lcm

CONS (Constants) Menu BLTIN

EDIT

MISC gcd

4

4Frac

EDIT k

USER Cc

ec

Rc

VOL

TIME

VOL m

CONV AREA Menu LNGTH AREA ft 2 m2

eval

VOL mi2

TIME in

4

Gc

Mp

Mn

-‘& g

Me

4

TEMP ft

4

H0

h

c

u

Ang

fermi

rod

fath

MASS FORCE PRESS ENRGY POWER 4 SPEED

-’& 4

yd

km

mile

nmile

in2

cm2

yd2

ha

lt-yr

4

-’' TIME km2

m0

-’ TEMP

CONV LNGTH (Length) Menu LNGTH AREA mm cm

x‡

-‘

CONV (Conversions) Menu LNGTH AREA

pEval

USER

CONS BLTIN (Built-In Constants) Menu BLTIN Na

%

TEMP acre

4

99APPX.DOC TI-86, Appendix, US English Bob Fedorisko Revised: 02/27/01 1:20 PM Printed: 02/27/01 1:26 PM Page 387 of 26

mil

388

Appendix -’(

CONV VOL (Volume) Menu LNGTH AREA liter gal

VOL qt

TIME pt

TEMP oz

4

CONV TIME Menu

-’)

LNGTH AREA sec mn

TIME day

VOL hr

TEMP yr

4

CONV TEMP (Temperature) Menu LNGTH AREA ¡C ¡F

VOL ¡K

CONV MASS Menu

TIME ¡R

in 3

ft 3

m3

week

ms

µs

ns

cup

4

-’*

TEMP

-’/&

MASS FORCE PRESS ENRGY POWER gm kg lb amu slug 4

CONV FORCE Menu

cm 3

ton

mton

-’/'

MASS FORCE PRESS ENRGY POWER N dyne tonf kgf lbf

CONV PRESS (Pressure) Menu

-’/(

MASS FORCE PRESS ENRGY POWER atm bar Nàm 2 lbàin 2 mmHg 4 mmH 2

CONV ENRGY (Energy) Menu

inHg

inH20

-’/)

MASS FORCE PRESS ENRGY POWER J cal Btu ft-lb kw-hr 4

eV

erg

I-atm

99APPX.DOC TI-86, Appendix, US English Bob Fedorisko Revised: 02/27/01 1:20 PM Printed: 02/27/01 1:26 PM Page 388 of 26

tsp

tbsp

ml

galUK

ozUK

Appendix -’/*

CONV POWER Menu

STRNG Menu "

sub

LIST Menu {

}

}

-” NAMES EDIT

NAMES

"

} NAMES EDIT sortA sortD min

TYPE

CONV BOOL

BASE TYPE Menu Õ-Ú Ü

TYPE ß

knot

-”(

LIST NAMES Menu OPS

{ fStat

} NAMES EDIT xStat yStat

OPS

-”)

The (Number) BASE Menu Õ-Ú

miàhr kmàhr

Eq4St St4Eq

4

OPS

OPS max

4

sum

-— BIT

-—'

CONV BOOL Ý Þ

4REAL

-”*

LIST OPS (Operations) Menu { dimL

SPEED ftàs màs

-“ lngth

List Editor Menu {

-’//&

CONV SPEED Menu

MASS FORCE PRESS ENRGY POWER hp W ftlbàs calàs Btuàm

389

BIT

prod

seq

li4vc

vc4li

4

Fill

4

Sorty

aug

cSum

Deltal

Select SetLE

Form

BASE Õ-Ú (Hexadecimal) Menu Õ Ö

TYPE ×

CONV BOOL Ø Ù

-—&

BIT Ú

BASE CONV (Conversions) Menu Õ-Ú 4Bin

TYPE 4Hex

CONV BOOL 4Oct 4Dec

99APPX.DOC TI-86, Appendix, US English Bob Fedorisko Revised: 02/27/01 1:20 PM Printed: 02/27/01 1:26 PM Page 389 of 26

Sortx

BIT

-—(

390

Appendix -—)

BASE BOOL (Boolean) Menu Õ-Ú and

TYPE or

CONV BOOL xor not

TEST (Relational) Menu ==

<

MEM (Memory) Menu RAM

DELET RESET

TOL



REAL

CPLX

MEM RESET Menu RAM ALL

DELET RESET MEM DFLTS

LIST

STAT (Statistics) Menu When you press - š ', the list editor and list menu are displayed.

CALC

EDIT

4

BIT

ƒ

ClrEnt

-™'

VECTR 4 MATRX STRNG

-™( TOL

CONV BOOL shftR shftL

-™

MEM DELET (Delete) Menu ALL

TYPE rotL





>

-—*

BASE BIT Menu Õ-Ú rotR

BIT

EQU

CONS PRGM

4

GDB

PIC

MEM RESET Are You Sure? Menu

ClrEnt

YES

NO



PLOT DRAW VARS

4

-š&

STAT CALC (Calculations) Menu CALC EDIT PLOT DRAW VARS OneVa TwoVa LinR LnR ExpR

FCST

4

PwrR

SinR

LgstR P2Reg P3Reg

4

P4Reg StReg

99APPX.DOC TI-86, Appendix, US English Bob Fedorisko Revised: 02/27/01 1:20 PM Printed: 02/27/01 1:26 PM Page 390 of 26

391

Appendix STAT PLOT Menu PLOT1 PLOT2 PLOT3

Plot Mark Menu PLOT1 PLOT2 PLOT3 › + ¦

STAT DRAW Menu CALC HIST

-š( PlOn

PLOT1 PLOT2 PLOT3 SCAT xyLINE MBOX

PlOn

PlOff BOX

PlOff

-š)

EDIT PLOT DRAW VARS SCAT xyLINE BOX MBOX

EDIT sx

PlOn HIST

- š ( ( &, ', or ( ) # ( &, ', or ( ) # # #

4 DRREG CLDRW DrawF STPIC RCPIC

STAT VARS (Statistical Result Variables) Menu CALC v

- š ( ( &, ', or ( ) #

Plot Type Menu

PlOff

PLOT DRAW VARS Sx w sy

CHAR (Character) Menu

-š*

4

Sy

Gx

Gx 2

Gy

Gy 2

4

Gxy

RegEq

corr

a

b

4

n

minX

maxX

minY

maxY

4

Med

PRegC

Qrtl1

Qrtl3

tolMe

~

|

4

¿

Ñ

ñ

Ç

ç



MISC GREEK INTL

Ñ, ñ, Ç, and ç are valid as the

first letter of a variable name.

CHAR MISC (Miscellaneous) Menu MISC GREEK INTL ? # &

%

'

4

-Ÿ& !

@

$

%, ' , and ! can be functions.

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392

Appendix CHAR GREEK Menu

All CHAR GREEK menu items are valid variable-name characters, including the first letter. p (- ~) is not valid as a character; p is a constant on the TI-86.

MISC GREEK INTL a b g

-Ÿ' @

d

4

H

q

l

m

r

4

G

s

ι

f

J

CHAR INTL (International Letter Symbols) Menu

-Ÿ(

MISC GREEK INTL

´

`

^

¨

Handling a Difficulty

If you cannot see anything on the screen, you may need to adjust the contrast (Chapter 1).

♦ ♦

To darken the screen, press and release -, and then press and hold $. To lighten the screen, press and release -, and then press and hold #.



If an error menu is displayed, follow the steps in Chapter 1. Refer to the Error Conditions section of the Appendix (page 393) for details about specific errors, if necessary.



If a checkerboard cursor ( Ä ) is displayed, then either you have entered the maximum number of characters in a prompt or memory is full. If memory is full, press - ™ ', select a data type, and then delete some items from memory (Chapter 17).



If the busy indicator (dotted line) is displayed in the top-right corner, a graph or program has paused; the TI-86 is waiting for input. Press b to continue or press ^ to break.



If the calculator does not seem to work at all, be sure the batteries are fresh and that they are installed properly. Refer to battery information in Chapter 1.

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Appendix

393

Error Conditions When the TI-86 detects an error, it displays an error message ERROR # type and the error menu. Chapter 1 describes how to correct an error. This section describes possible causes for the errors and examples. To find the proper arguments for a function or instruction, as well as restrictions on those arguments, refer to Chapter 20: A to Z Function and Instruction Reference. Errors 1 through 5 do not occur during graphing. The TI-86 allows for undefined values on a graph.

01 OVERFLOW

♦ ♦

You attempted to enter a number that is beyond the calculator’s range. You attempted to execute an expression with a result that is beyond the calculator’s range.

02 DIV BY ZERO

♦ ♦

You attempted to divide by zero. You attempted a linear regression with a vertical line.

03 SINGULAR MAT



You attempted to use a singular matrix (determinate = 0) as the argument for L1 , Simult, or LU. You attempted a regression with at least one inappropriate list. You attempted to use a matrix with repeated eigenvalues as the argument for exp, cos, or sin.

♦ ♦ 04 DOMAIN

♦ ♦

You attempted to use an argument that is out of the range of valid values for the function or instruction. You attempted a logarithmic or power regression with a Lx or an exponential regression with a Ly.

05 INCREMENT

The increment in seq is 0 or has the wrong sign; the increment for a loop is 0.

06 BREAK

You pressed ^ to break a program, DRAW instruction, or expression evaluation.

07 SYNTAX

You entered a value; look for misplaced functions, arguments, parentheses, or commas; check the syntax description in the A to Z Reference.

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394

Appendix 08 NUMBER BASE

♦ ♦

09 MODE

You attempted to store to a window variable of a noncurrent graphing mode. or to use an instruction valid only in noncurrent graphing modes; for example, using DrInv in Pol, Param, or DifEq graphing mode.

10 DATA TYPE

♦ ♦ ♦ ♦ ♦

You entered an invalid digit in a number base, such as 7Ü. You attempted an operation that is not allowed in Bin, Oct , or Hex base mode.

You entered a value or variable that is an inappropriate data type. You entered an argument that is an inappropriate data type for a function or an instruction, such as a program name for sortA. In an editor, you entered a data type that is not allowed; check the appropriate chapter. You attempted to store data to a protected data type, such as a constant, program, picture, or graph database. You attempted to store inappropriate data to a restricted built-in variable, such as the list names xStat, yStat, and fStat.

11 ARGUMENT

You attempted to execute a function or instruction without all the arguments.

12 DIM MISMATCH

You attempted to use two or more lists, matrices, or vectors as arguments, but the dimensions of all arguments are not equal, such as {1,2}+{1,2,3}.

13 DIMENSION

♦ ♦ ♦

14 UNDEFINED

You are referencing a variable that currently is not defined.

15 MEMORY

Memory is insufficient to perform the desired command; you must delete items from memory (Chapter 17) before executing this command.

16 RESERVED

You attempted to use a built-in variable inappropriately.

17 INVALID

You attempted to reference a variable or use a function where it is not valid.

You entered an argument with an inappropriate dimension. You entered a matrix or vector dimension < 1 or > 255 or a noninteger. You attempted to invert a matrix that is not a square matrix.

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Appendix 18 ILLEGAL NEST

You attempted to use an invalid function in an argument for seq( or a CALC function; for example, der1(der1(x^3,x),x)).

19 BOUND

You defined an upper bound that is less than the specified lower bound or a lower bound that is greater than the specified upper bound.

20 GRAPH WINDOW

♦ ♦

One or more window variable values is incompatible with the others for defining the graph screen; for example, you defined xMax < xMin. Window variables are too small or too large to graph correctly; for example, you attempted to zoom out beyond the calculator’s range.

21 ZOOM

A ZOOM operation resulted in an error; you attempted to define ZBOX with a line.

22 LABEL

In programming, the Goto instruction label is not defined with a Lbl instruction.

23 STAT

♦ ♦ ♦

Errors 26 through 29 occur during the solving process. Examine a graph of the function or a graph of the variable vs. leftNrt in the SOLVER. If the equation has a solution, change bounds andàor the initial guess.

395

You attempted a stat calculation with at least one inappropriate list, such as a list with less than two data points. At least one element of a frequency list is < 0. (xMax N xMin)àxScl  63 must be true when plotting a histogram.

24 CONVERSION

When converting measurements, the units are incompatible, as in volts to liters.

25 SOLVER

♦ ♦

26 SINGULARITY

In the solver editor, the equation contains a singularity, which is a point at which the function is not defined.

27 NO SIGN CHNG

The solver did not detect a sign change.

28 ITERATIONS

The solver has exceeded the maximum permitted number of iterations.

29 BAD GUESS

♦ ♦

In the solver editor, the equation does not contain a variable. You attempted to graph with the cursor positioned on bound.

The initial guess was outside the specified bounds. The initial guess and several points around the guess are undefined.

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396

Appendix 30 DIF EQ SETUP

In DifEq graphing mode, equations in the equation editor must be from Q'1 to Q'9 and each must have an associated initial condition from Q[1 to Q[9.

31 DIF EQ MATH

The step size used by the fitting algorithm has become too small; check the equations and initial values; try a larger value for the window variable difTol; try changing tMin or tMax to examine a different region of the solution.

32 POLY

All coefficients are 0.

33 TOL NOT MET

The algorithm cannot return a result accurate to the requested tolerance.

34 STAT PLOT

You attempted to display a stat plot that references an undefined list.

35 AXES

You attempted to plot a DifEq graph with improper axes set.

36 FLDàORDER

♦ ♦

You attempted to plot a 2nd-order or higher differential equation with SlpFld field format set; change field format or modify the order. You attempted to plot a 3rd-order or higher differential equation with DirFld field format set; change field format or modify the order.

37 LINK MEMORY FULL

You attempted to transmit an item with insufficient available memory in the receiving unit; skip the item or cancel the transmission.

38 LINK TRANSMISSION ERROR



39 LINK DUPLICATE NAME

Unable to transmit item; check to see that the cable is firmly connected to both units and the receiving unit is ready to receive data (Chapter 18). ♦ You pressed ^ to break during transmission. You attempted to transmit an item when an item with the same name already exists in the receiving unit.

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Appendix

397

Equation Operating System (EOS™) The Equation Operating System (EOS) governs the order of evaluation on the TI-86. Calculations within parentheses are evaluated first, and then EOS evaluates functions within an expression in this order: Within a priority level, EOS evaluates functions from left to right.

Multi-argument functions, such as nDeriv(A2,A,6), are evaluated as they are encountered.

TI-86 implied multiplication rules differ from those of the TI-85. For example, the TI-86 evaluates 1à2x as (1à2)¹x, while the TI-85 evaluates 1à2x as 1à(2¹x).

1st

Functions that are entered after the argument, such as 2, M1, !, ¡, r, and conversions

2nd

Powers and roots, such as 2^5 or 5x‡32

3rd

Single-argument functions that precede the argument, such as ‡( , sin( , or log(

4th

Permutations (nPr) and combinations (nCr)

5th

Multiplication, implied multiplication, and division

6th

Addition and subtraction

7th

Relational functions, such as > or 

8th

Logic operator and

9th

Logic operators or and xor

Implied Multiplication The TI-86 recognizes implied multiplication, so you need not press M to express multiplication in all cases. For example, the TI-86 interprets 2p, 4sin(46), 5(1+2), and (2¹5)7 as implied multiplication. Parentheses All calculations inside a pair of parentheses are completed first. For example, in the expression 4(1+2), EOS evaluates 1+2 inside the parentheses first, and then multiplies 3 by 4.

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Appendix

You can omit the close parenthesis ( ) ) at the end of an expression. All open parenthetical elements are closed automatically at the end of an expression. This is also true for open parenthetical elements that precede the store or display-conversion instructions. Open parentheses after list names, matrix names, or equation function names are not interpreted as implied multiplication. Arguments that follow these open parentheses are specified list elements, matrix elements, or values for which to solve the equation function.

TOL (The Tolerance Editor)

-™)

On the TI-86, the computational accuracy of some functions is controlled by the variables tol and d. The values stored to these variables may affect the speed at which the TI-86 calculates or plots. The variable tol defines the tolerance in calculating the functions fnInt(, fMin(, fMax(, and arc(, and the GRAPH MATH operations Gf(x), FMIN, FMAX, and ARC (Chapter 6). tol must be a positive value ‚ 1EL12. The value stored to d must be a positive real number. d defines the step size the TI-86 uses to calculate the functions arc in dxNDer mode; nDer; and the operations dyàdx, dràdq, dyàdt, dxàdt, INFLC, TANLN, and ARC, all in dxNDer mode (Chapter 6). To store a value to tol or d on the home screen or in a program, use X. You can select tol and d from the CATALOG. Also, you can enter tol directly and select d from the CHAR GREEK menu.

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Appendix

399

Computational Accuracy To maximize accuracy, the TI-86 carries more digits internally than it displays. Values are stored in memory using up to 14 digits with a 3-digit exponent. ♦ You can store values up to 12 digits long to most window variables. To xScl, yScl, tStep, and qStep, you can store values up to 14 digits long. ♦ When a value is displayed, the displayed value is rounded as specified by the mode setting (Chapter 1), with a maximum of 12 digits and a 3-digit exponent. ♦ Chapter 4 describes calculations in hexadecimal, octal, and binary number bases.

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400

Appendix

Support and Service Information Product Support Customers in the U.S., Canada, Puerto Rico, and the Virgin Islands For general questions, contact Texas Instruments Customer Support: phone: e-mail:

1.800.TI.CARES (1.800.842.2737) [email protected]

For technical questions, call the Programming Assistance Group of Customer Support: phone:

1.972.917.8324

Customers outside the U.S., Canada, Puerto Rico, and the Virgin Islands Contact TI by e-mail or visit the TI Calculator home page on the World Wide Web. e-mail: [email protected] Internet: education.ti.com

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Appendix

401

Product Service Customers in the U.S. and Canada Only Always contact Texas Instruments Customer Support before returning a product for service. Customers outside the U.S. and Canada Refer to the leaflet enclosed with this product or contact your local Texas Instruments retailer/distributor.

Other TI Products and Services Visit the TI Calculator home page on the World Wide Web. education.ti.com

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402

Appendix

Warranty Information Customers in the U.S. and Canada Only One-Year Limited Warranty for Commercial Electronic Product This Texas Instruments electronic product warranty extends only to the original purchaser and user of the product. Warranty Duration. This Texas Instruments electronic product is warranted to the original purchaser for a period of one (1) year from the original purchase date. Warranty Coverage. This Texas Instruments electronic product is warranted against defective materials and construction. THIS WARRANTY IS VOID IF THE PRODUCT HAS BEEN DAMAGED BY ACCIDENT OR UNREASONABLE USE, NEGLECT, IMPROPER SERVICE, OR OTHER CAUSES NOT ARISING OUT OF DEFECTS IN MATERIALS OR CONSTRUCTION. WARRANTY DISCLAIMERS. ANY IMPLIED WARRANTIES ARISING OUT OF THIS SALE, INCLUDING BUT NOT LIMITED TO THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE, ARE LIMITED IN DURATION TO THE ABOVE ONE-YEAR PERIOD. TEXAS INSTRUMENTS SHALL NOT BE LIABLE FOR LOSS OF USE OF THE PRODUCT OR OTHER INCIDENTAL OR CONSEQUENTIAL COSTS, EXPENSES, OR DAMAGES INCURRED BY THE CONSUMER OR ANY OTHER USER. Some states/provinces do not allow the exclusion or limitation of implied warranties or consequential damages, so the above limitations or exclusions may not apply to you. Legal Remedies. This warranty gives you specific legal rights, and you may also have other rights that vary from state to state or province to province. Warranty Performance. During the above one (1) year warranty period, your defective product will be either repaired or replaced with a reconditioned model of an equivalent quality, (at TI’s option) when the product is returned, postage prepaid, to Texas Instruments Service Facility. The warranty for the repaired or replacement unit will continue for the warranty of the original unit or six (6) months, whichever is longer. Other than the postage requirement, no charge will be made for such repair and/or replacement. TI strongly recommends that you insure the product for value prior to mailing. Software. Software is licensed, not sold. TI and its licensors do not warrant that the software will be free from errors or meet your specific requirements. All software is provided “AS IS.” Copyright. The software and any documentation supplied with this product are protected by copyright.

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Appendix

403

Australia & New Zealand Customers only One-Year Limited Warranty for Commercial Electronic Product This Texas Instruments electronic product warranty extends only to the original purchaser and user of the product. Warranty Duration. This Texas Instruments electronic product is warranted to the original purchaser for a period of one (1) year from the original purchase date. Warranty Coverage. This Texas Instruments electronic product is warranted against defective materials and construction. This warranty is void if the product has been damaged by accident or unreasonable use, neglect, improper service, or other causes not arising out of defects in materials or construction. Warranty Disclaimers. Any implied warranties arising out of this sale, including but not limited to the implied warranties of merchantability and fitness for a particular purpose, are limited in duration to the above one-year period. Texas Instruments shall not be liable for loss of use of the product or other incidental or consequential costs, expenses, or damages incurred by the consumer or any other user. Some jurisdictions do not allow the exclusion or limitation of implied warranties or consequential damages, so the above limitations or exclusions may not apply to you. Legal Remedies. This warranty gives you specific legal rights, and you may also have other rights that vary from jurisdiction to jurisdiction. Warranty Performance. During the above one (1) year warranty period, your defective product will be either repaired or replaced with a new or reconditioned model of an equivalent quality (at TI’s option) when the product is returned to the original point of purchase. The repaired or replacement unit will continue for the warranty of the original unit or six (6) months, whichever is longer. Other than your cost to return the product, no charge will be made for such repair and/or replacement. TI strongly recommends that you insure the product for value if you mail it. Software. Software is licensed, not sold. TI and its licensors do not warrant that the software will be free from errors or meet your specific requirements. All software is provided “AS IS.” Copyright. The software and any documentation supplied with this product are protected by copyright.

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404

Appendix

All Customers outside the U.S. and Canada For information about the length and terms of the warranty, refer to your package and/or to the warranty statement enclosed with this product, or contact your local Texas Instruments retailer/distributor.

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Index " (string), 216, 227 " (List Editor menu), 156 ! (factorial), 294 ¶, 362 ‚ (greater than or equal to), 56, 301  (less than or equal to), 55, 312 ƒ (not equal to), 56, 326 p (pi), 48 ‡ (square root), 360 ˆ (square root) key, 48 v (statistical result variable), 193 w (statistical result variable), 193 L1 (inverse), 48, 309 ¶dim, 184, 281 ¶dimL, 282 ‰f(x) (function numerical integral), 96, 98 @Tbl (table step), 113 sx (statistical result variable), 193

Gx 2 (statistical result variable), 193 sy (statistical result variable), 193 % (percent), 52, 334 < (less than), 55, 312 = (assign to), 270 = (equals), 290 == (relational equals), 55, 291 > (greater than), 55, 300 [ ], 319, 369 ^ (exponent), 48 { }, 316 10^ (10 raised to n power), 48, 337

A abs (absolute value), 49, 71, 175, 185, 267 addition (+), 267 ALL, 43, 232 ALLN, 77 ALL+, 77 ALPHA character, 22 ALPHA cursor, 22

alpha cursor, 22 ALPHA key, 21 ALPHA-lock, 22, 44 canceling, 22 setting, 22 and (Boolean), 69, 268 angle, 71, 175, 185, 269 expressed in degrees, 51 angle modes, 35 angle values, 35 Ans (last answer), 29, 30, 41, 269 answer displaying, 19 storing to a variable, 41 APD. See Automatic Power Down ARC, 96, 98 arc(, 54, 269 argument, 25 Asm (assembly language program), 269 AsmComp (compile assembly language program), 226, 270 AsmPrgm (assembly language program), 226, 270

99INDEX.DOC TI-86, Index, US English Bob Fedorisko Revised: 02/13/01 2:51 PM Printed: 02/27/01 1:29 PM Page 405 of 15

assembly language programs, 225 assignment, 270 attached formulas executing, 164 resolving errors, 165 attached-formula list comparing, 163 creating, 162 editing elements, 166 aug(, 160, 184, 270 Automatic Power Down, 17 automatic regression equation storage, 191 AXES, 137 Axes editor, 137 field formats, 137 Axes(, 271 AxesOff, 84, 271 AxesOn, 84, 271

B

Ü (binary), 271 backup battery, 16

406

Index

BASE Õ-Ú (Hexadecimal) menu, 67 BASE BIT menu, 69 BASE BOOL (Boolean) menu, 68 BASE CONV (Conversion) menu, 68 BASE menu, 66 BASE TYPE menu, 67 base type symbol, 67 batteries, 2, 16-18 battery compartment, 16 BCKUP (memory backup), 237 Bin (binary), 35, 272 4Bin (to binary), 68, 272 binary integer, 271 binary number base, 35, 66 Boolean operators, 68, 268, 325, 328, 370 bound={L1E99,1E99}, 204 bounds, 204 BOX (GRAPH ZOOM menu), 14, 92, 93 Box (stat plot), 272 BOX (ZOOM menu), 208 break (program), 222 BREAK menu, 26

built-in constants, 58 built-in variables, 39, 45, 138 busy indicator, 26, 85

C CALC (Calculus) menu, 54 calculating derivatives, 7 calculation interrupting, 26 calculus functions, 54 CATALOG, 25, 38 Quick-Find Locator, 262 CATLG (CATALOG), 43 CATLG-VARS (CATALOG Variables) menu, 43 changing TI-86 settings, 39 CHAR (Character) menu, 45 CHAR GREEK menu, 46 CHAR INTL (International) menu, 46 CHAR MISC (Miscellaneous) menu, 46 characters, 19 alpha, 22 blue, 21, 22 case, 22

characters (continued) deleting, 23 entering, 21 second, 22 yellow, 21 check RAM screen, 230 CIRCL (circle), 105, 106 Circl(, 273 circles drawing, 106 CLDRW (clear drawing), 103, 105, 273 clearing CUSTOM menu items, 45 clearing ENTRY storage area, 29 ClLCD (clear LCD), 216, 273 ClrEnt (clear entry), 232, 273 ClTbl (clear table), 114, 216, 273 cnorm (column norm), 183, 273 command line, 220 complements (binary numbers), 66 complex matrix, 180 Complex Number menu, 71 complex number modes, 35

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complex number variables, 43 complex numbers, 29, 70 as list elements, 156 displaying as result, 5 entering, 20 in results, 70 separator, 70 using in expressions, 71 complex values, 48 concatenation (+), 274 cond (condition number), 183, 274 conj (complex conjugate), 71, 175, 185, 275 connecting instructions, 235 CONS (constants), 43 CONS (Constants) menu, 58 CONS BLTIN (Built-In Constants) menu, 58 CONS EDIT menu, 60 consecutive entries, 26 Constant Memory feature, 17, 34 constants, 59 built-in, 58 defined, 58 name, 61 user-created, 58, 60

Index contrast adjusting, 2, 18 CONV (Conversions) menu, 62 CONV AREA menu, 63 CONV ENRGY (Energy) menu, 64 CONV FORCE menu, 64 CONV LNGTH (Length) menu, 63 CONV MASS menu, 64 CONV POWER menu, 64 CONV PRESS (Pressure) menu, 64 CONV SPEED menu, 64 CONV TEMP (Temperature) menu, 8, 63 CONV TIME menu, 63 CONV VOL (Volume) menu, 63 conversions 4Bin, 272 4Dec, 279 4DMS, 51, 285 4Frac, 52, 298 4Hex, 303 4Oct, 327 4Pol, 336 4REAL, 156

conversions (continued) 4Rec, 343 4Sph, 360 Eq4St, 227 li4vc, 160 St4Eq(, 227, 361 vc4li, 160 converting a value expressed as a rate, 65 converting Fahrenheit to Celsius, 8 converting units of measure, 61 CoordOff, 84, 275 CoordOn, 84, 275 copying variable value, 41 corr (correlation coefficient), 193 cos (cosine), 48, 186, 276 cos L1 (arccosine), 48, 276 cosh (hyperbolic cosine), 51, 277 cosh L1 (inverse hyperbolic cosine), 51, 277 CPLX (complex number variables), 43, 71 cross(, 173, 277

cSum( (cumulative sum), 160, 278 current entry, 19 clearing, 23 current item, 38 cursor, 17, 22 ALPHA, 22 alpha, 22 changing, 23 direction keys, 23 entry, 22 free-moving, 128, 144, 205 full, 22 insert, 22 location, 19, 20, 21, 25 moving, 23 second, 22 selection, 38 trace, 90 curves drawing, 107 CUSTOM menu, 44 clearing items, 45 copying items, 44 Customer Support, 392 4Cyl (to cylindrical), 174, 278

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407

CylV (cylindrical vector coordinate mode), 36, 278

D

Þ (decimal), 278 data type selection screen, 42 Dec (decimal number base mode), 278 Dec (decimal), 35, 65 4Dec (to decimal), 279 decimal, 20 decimal mode, 34, 35, 65 fixed (012345678901), 35 floating, 35 decimal number, 278 decimal number base, 35 decimal point, 35 degree angle mode, 35, 75, 279 degree complex-number mode, 70 degree entry (¡), 279 degrees¡, 51 degrees/minutes/seconds form, 51 DELc (delete column), 179 DELET, 60

408

Index

DELf (delete function), 77 DELi (delete element), 170 DELr (delete row), 179 Deltalst( (delta list), 160, 279 DelVar( (delete variable), 219, 280 der1( (first derivative), 54, 280 der2( (second derivative), 54, 280 derivatives calculating, 7 det (determinant), 183, 281 DFLTS (defaults), 232 DifEq (differential equation mode), 35, 74, 239, 281 differential equation editor, 134 differential equation graphs, 74 displaying, 138 drawing, 145 mode, 35 differential equations changing to first order, 142 defining graph, 132 drawing solutions, 148 DrEqu(, 287 editor, 134 EXPLR, 148

differential equations (continued) graphing, 132, 137, 139, 141, 142 initial conditions editor, 136 mode, 144 Q'n equation variables, 135 setting axes, 137 setting graph format, 133 setting graphing mode, 132 solving, 139 tracing, 144 using EVAL, 150 window variables, 135 differentiation modes, 36 difTol (tolerance), 136 dim (dimension), 173, 184, 281 dimL (dimension of list), 159, 282 DirFld (direction field), 134, 282 Disp (display), 216, 283 DispG (display graph), 283 display, 17 display contrast adjusting, 17, 18 displaying a menu, 31 DispT (display table), 284

DIST (distance), 96, 98 division (/), 284 division symbol, 3 4DMS (to degrees/ minutes/seconds), 51, 285 dot(, 173, 285 dr/dq, 122 DRAW, 75, 88 DrawDot, 84, 285 DrawF (draw function), 103, 107, 286 drawing circles, 106 differential equation graphs, 145 freehand points, lines, curves, 107 function, tangent line, inverse function, 107 line segments, 105 lines, 105, 106 parametric graphs, 130 points, 108 polar graphs, 122 drawing tools, 101 drawings clearing, 103

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drawings (continued) recalling, 102 saving, 102 DrawLine, 84, 286 DrEqu( (draw equation), 145, 287 DrInv (draw inverse), 103, 107, 287 DS<( (decrement and skip), 219, 288 DUPLICATE NAME menu, 241 dx/dt, 130 dxDer1 (exact differentiation), 36, 75, 288 dxNDer (numeric differentiation), 36, 75, 288 dy/dt, 130 dy/dx, 96, 99, 130

E E (exponent), 48, 292 e^ (e raised to power), 288 editing equations, 205 editor menu, 33 eigVc (eigenvector), 183, 289 eigVl (eigenvalue), 183, 289

Index element matrix, 181 ellipsis at end of line, 19 in matrix row, 179 Else, 218, 306 e-mail address (TI Customer Support), 392 End, 218, 290, 297, 306 Eng (engineering notation), 34, 20, 290 entry executing, 19 storing to, 29 entry cursor, 18, 22, 23 [ENTRY] key, 19 ENTRY Storage Area, 28, 29 EOS. See Equation Operating System Eq4St( (equation to string), 227, 290 eqn (equation) variable, 54, 203, 205 EQU (equation variables), 43 equal (=), 290 equal to (==), 291

equation entering, 203 evaluating, 122, 130 equation coefficients storing to a variable, 210 equation editor, 74, 75, 76, 80 entering a function, 77 graph styles, 77 parametric, 126 polar, 118 Equation Editor menu, 76 Equation Operating System, 397 equation results storing to a variable, 210 equation solver, 40, 202 graph tools, 207 equation storage automatic regression, 191 equation variables, 40, 43, 78 equation-entry editor, 203 equations editing, 205 solving, 206 error conditions, 393 error menu, 31 error message, 27

error type, 27 errors, 17, 27 correcting, 27 diagnosing, 27 from attached formulas, 165 EStep, 136 Euler method, 133, 291 eval, 52, 76, 88, 101, 122, 130, 150, 291 evalF(, 54, 292 evaluating a function for x, 101 evaluating equations, 122, 130 e x (constant e raised to a power), 48 exact differentiation, 36 EXIT (cancel data transmission), 241 exiting a menu, 6, 33 exp variable, 54, 203 EXPLR (explore), 148 exponent (å), 292 ExpR (exponential regression), 190, 293 expression, 18, 20, 24, 25, 26, 30, 48 editing, 4 entering, 24

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409

expression (continued) entering a list, 153 evaluating, 29, 30 using a complex number, 71 using a vector, 172 using matrix, 181

F factorial (!), 50, 294 Fahrenheit converting to Celsius, 8 family of curves graphing, 86 in parametric graphs, 129 in polar graphs, 120 fcstx (forecast x), 294 fcsty (forecast y), 294 feature symbol, 39 field formats, 134 Fill, 184 Fill(, 160, 173, 295 Fix, 295 FldOff (slope and direction fields off), 134, 295 fldPic (field) variable, 138 Float, 35, 295

410

Index

FMAX (function maximum), 96, 97 fMax( (function maximum), 54, 296 FMIN (function minimum), 96, 97 fMin( (function minimum), 54, 296 fnInt( (function integral), 54, 296 FnOff (functions off), 296 FnOn (functions on), 297 For(, 218, 297 Form(, 161, 298 FORMT (graph format), 76 formulas attaching, 163 attaching to list name, 162 detaching, 166 fPart (fractional part), 49, 176, 186, 298 4Frac (to fractions), 52, 298 fraction, 3, 19 free-moving cursor, 84, 144 parametric graphs, 128 polar graphs, 119 fStat (frequency list), 189

full cursor, 22 Func (function mode), 35, 74, 239, 299 function graphs, 73, 74 mode, 35 functions, 25, 38 deleting, 77 deselecting, 13 drawing, 107 entering, 25 entering in the equation editor, 76, 77, 78 evaluating, 101 keyboard, 48 plotting, 11 tracing, 11 using with lists, 5, 161

G gcd( (greatest common denominator), 52, 299 GDB (graph database), 43 GDB variable, 102 Get(, 299 getKy (get key), 216, 300 key code diagram, 217

GOTO, 26, 27, 300 Goto (PRGM CTL menu), 219, 224 graph, 75 defining, 74 displaying, 85 family of curves, 86 interrupting, 26 modifying, 85 pausing, 85 shading, 104 stopping, 85 GRAPH (Solver menu), 206 graph database (GDB), 102 recalling, 76 GRAPH DRAW menu, 75, 103, 122, 145 graph format differential equations, 133, 137 parametric graphs, 128 polar graphs, 119 screen, 76 setting, 83 GRAPH LINK, 235 GRAPH MATH menu, 75, 95, 122, 130

99INDEX.DOC TI-86, Index, US English Bob Fedorisko Revised: 02/13/01 2:51 PM Printed: 02/27/01 1:29 PM Page 410 of 15

GRAPH MATH operations effect of other settings, 96 using ‰f(x), DIST, or ARC, 98 using dy/dx or TANLN, 99 using ISECT, 100 using ROOT, FMIN, FMAX, or INFLC, 97 using YICPT, 100 GRAPH menu, 27, 31, 75, 88, 117, 126, 133 graph modes, 35 setting, 74 differential equations, 144 function, parametric, 126 polar, 35, 117 graph screen, 75 setting window variables, 81 graph screen dimensions, 75 graph styles, 79 changing, 10 GrStl(, 302 setting, 79 graph tools in differential equation graphs, 144 in equation solver, 207

Index graph tools (continued) in parametric graphs, 128 in polar graphs, 119 graph zoom defining custom, 93 defining screen, 92 setting zoom factors, 93 Smart Graph, 94 zooming in, 92, 93 zooming out, 92, 93 GRAPH ZOOM menu, 75, 91, 147 graphing accuracy, 89 greater than (>), 300 greater than or equal to (‚), 301 grid points, 84 GridOff, 84, 301 GridOn, 84, 302 GrStl( (graph style), 220, 302 Guess, 204 in interactive solver editor, 205

H

ß (hexadecimal), 302 Hex (hexadecimal), 35, 302

4Hex (to hexadecimal), 68, 303 hexadecimal characters menu, 67 hexadecimal number base, 35, 66 Hist (histogram), 303 home screen, 17, 18, 23, 24, 26, 27 displaying entries and answers, 18 Horiz, 304 HORIZ (horizontal line), 105, 106 hyperbolic functions, 51

I IAsk, 304 IAuto, 304 ident (identity), 184, 304 If, 218, 305, 306 imag (imaginary), 71, 175, 185, 306 imaginary portion of complex number, 71 implied multiplication, 397 INFLC (inflection point), 96, 97

INITC (initial conditions), 136 InpSt, 217, 307 Input (PRGM I/O menu), 216, 307 Input CBLGET, 216 INSc (insert column), 179 insert cursor, 22, 23 canceling, 23 INSf (insert function), 77 INSi (insert element), 170 INSr (insert row), 179 installing batteries, 16 instructions, 25 entering, 25 executing, 19 int (integer), 49, 176, 186, 308 integer part, 49 integer part of real numbers displaying, 6 inter( (interpolate), 309 interactive-solver editor, 204 bounds, 204 international letters, 46 Internet downloading programs, 235 e-mail address (TI Customer Support), 392

99INDEX.DOC TI-86, Index, US English Bob Fedorisko Revised: 02/13/01 2:51 PM Printed: 02/27/01 1:29 PM Page 411 of 15

411

interpolate/extrapolate editor, 53 interrupting a calculation, 26 interrupting a graph, 26, 27 interrupting a program, 222 inverse, 309 inverse function drawing, 107 IPart (integer part), 6, 49, 176, 186, 309 IS>( (increment and skip), 219, 310 ISECT (intersection), 96, 100 items on menus, 31

K keys, 48 2nd, 21 ALPHA, 21 primary function, 19, 21, 22 key code diagram, 217

L LabelOff, 84, 310 LabelOn, 84, 310

412

Index

last answer, 28, 29 storing to variable, 3 last entry, 26, 28 Lbl (label), 219, 224, 311 lcm( (least common multiple), 52, 311 LCust( (load custom menu), 220, 311 leftNrt, 202 length of segment of curve, 54 less than (<), 312 less than or equal to (), 312 LgstR (logistic regression), 190, 193, 313 li4vc (list to vector), 160, 174, 316 LINE, 104, 105 Line(, 314 Lines drawing, 107 LINK menu, 236 LINK SEND menu, 236 LINK SEND85 menu, 239 linking instructions, 235 linking options, 234 LinR (linear regression), 190, 315

list, 29, 43, 52 as an argument, 161 attached formulas, 165 attaching formula, 162, 166 braces { }, 316 comparing, 163 creating, 157 deleting an element, 158 deleting from memory, 154 detaching formulas, 166 displaying list elements, 154 editing elements, 166 entering in an expression, 153 inserting, 157 removing from list editor, 158 storing, 154 uses, 152 using with function, 5 list editor, 31, 67, 156, 188 attaching formulas, 163, 164 removing a list, 158 List Editor menu, 156 list element complex, 156 deleting, 158

list element (continued) displaying, 155, 158 editing, 158 storing a value to, 155 list entry { }, 316 LIST menu, 152 list names, 43 LIST NAMES menu, 153, 189 LIST OPS menu, 159 ln (natural log), 48, 316 lngth (length of string), 227, 316 LnR (logarithmic regression), 190, 317 log, 48, 318 low-battery message, 16, 18 lower menu, 32 LU( (lower-upper), 183, 318

MATH menu, 31, 49 MATH MISC (Miscellaneous) menu, 52 MATH NUM (Number) menu, 31, 49 MATH PROB (Probability) menu, 50 mathematical functions, 48 using with lists, 161 with a matrix, 185 matrix, 29 brackets [ ], 180, 319 creating, 178, 180 defined, 178 deleting from memory, 180 displaying elements, rows, submatrices, 181 editing using X, 182

M

names, 43 using in expression, 181 using math functions, 185 Matrix Editor menu, 179 matrix entry [ ], 319 MATRX (matrix names), 43 MATRX (Matrix) menu, 178 MATRX CPLX (Complex) menu, 185

Macintosh linking to, 235 MATH, 75 MATH (Graph menu), 88 MATH ANGLE menu, 51 MATH HYP (Hyperbolic) menu, 51

99INDEX.DOC TI-86, Index, US English Bob Fedorisko Revised: 02/13/01 2:51 PM Printed: 02/27/01 1:29 PM Page 412 of 15

Index MATRX MATH menu, 183 MATRX NAMES menu, 178 MATRX OPS (Operations) menu, 184 max(, 49, 160, 319 maximum characters, 22 maxX, 193 maxY, 193 MBox, 319 Med (median), 193 MEM (clear memory), 232 MEM (Memory) menu, 29, 230 MEM RESET menu, 232 MEM DELET (Delete) menu, 231 MEM FREE (available memory), 230 memory, 16, 17, 22, 28, 29, 223 available, 230 deleting items, 231 resetting, 3, 232 memory backup initiating, 237 overwrite warning, 237 menus displaying, 31 exiting, 6

menus (continued) in editors, 33 keys, 32 lower, 32 removing, 6, 33 selecting items, 32 upper, 33 menu map, 380 Menu(, 219, 320 min(, 49, 160, 320 minX, 193 minY, 193 mod(, 49, 320 mode settings, 19, 20, 70 changing, 34 displaying, 34 number base, 65 modulo, 49 mRAdd, 184 mRAdd(, 321 multiple entries retrieving, 29 multiplication (¹), 321 multR( (multiply row), 184, 322

N n (statistical results variable), 193 natural log, 48 nCr (number of combinations), 50, 322 nDer( (numerical derivative), 54, 323 negation symbol (L), 20 negative numbers entering, 19 norm, 173, 183, 323 Normal, 34, 324 not (Boolean), 66, 69, 325 not equal to (ƒ), 326 notation modes, 34 engineering, 34 normal, 34 scientific, 34 notation of displayed answers, 20 nPr (number of permutations), 50, 326 number base, 65 designators, 65 ranges, 66

99INDEX.DOC TI-86, Index, US English Bob Fedorisko Revised: 02/13/01 2:51 PM Printed: 02/27/01 1:29 PM Page 413 of 15

413

type, designating, 67 modes, 35 numbers entering, 19 numeric differentiation, 36 numerical derivative, 54

O

Ý, 326 Oct (octal), 35, 327 4Oct (to octal), 327 octal integer, 326 octal number base, 35, 66 OneVa (OneVar), 189, 191, 327 operation second, 22 operator entering, 25 or (Boolean), 69, 328 order of operations, 56 order-of-evaluation rules, 20, 62 Outpt(, 217, 329 OVERW (overwrite), 241

414

Index

P P2Reg (quadratic regression), 190, 330 P3Reg (cubic regression), 190, 331 P4Reg (quartic regression), 190, 332 panning, 90 Par, 74 Param (parametric mode), 35, 239, 333 parametric equation deleting, 127 graphing, 126 selecting and deselecting, 127 parametric graphs, 74 default graph style, 126 defining, 125 displaying, 128 drawing, 130 equation editor, 126 free-moving cursor, 128 graph format, 128 graph tools, 128

mode, 35, 126 tracing, 128 window variables, 127 Zoom, 129 parentheses, 20, 25, 56, 61, 397 pause, 26, 333 Pause (PRGM CTL menu), 219 pause indicator, 26 PC linking to, 235 PEN, 105 percent (%), 334 permutations of items, 50 pEval(, 52, 334 phone (TI Customer Support), 392 pi, 59 PIC (picture names), 43 PIC variable entering, 76 storing graph, 102 pictures recalling, 102 saving, 102 pixel resolution for function graphs, 81 PlOff (plot off), 195, 334

PlOn (plot on), 195, 334 PLOT1, 195 Plot1(, 335 PLOT2, 195 Plot2(, 335 PLOT3, 195 Plot3(, 335 plotting functions, 9, 11 plotting statistical data, 194 points drawing, 108 turning on and off, 108 Pol (polar mode), 35, 74, 239, 336 4Pol (to polar), 71, 174, 336 polar angle of complex number, 72 polar complex (), 336 polar complex mode, 35, 336 polar complex number form, 20, 70 polar equation tracing, 120 polar graphs, 74, 84 default graph style, 118 defining, 117 displaying, 119

99INDEX.DOC TI-86, Index, US English Bob Fedorisko Revised: 02/13/01 2:51 PM Printed: 02/27/01 1:29 PM Page 414 of 15

drawing, 122 equation editor, 118 free-moving cursor, 119 graph format, 119 graph tools, 119 polar graphs (continued) mode, 35 trace cursor, 120, 121 tracing, 120 window editor, 118 Zoom, 121 PolarC (polar complex mode), 35, 336 PolarGC (polar graph coordinates), 84, 336 poly, 337 polynomial coefficient storing to a variable, 212 polynomial root storing to a variable, 212 polynomial root-finder, 211 polynomial value, 52 power of 10 (10^), 20, 34, 337 PRegC, 193 previous entries, 8 re-executing, 19 retrieving, 28

Index reusing, 28 PRGM (program names), 43 PRGM CTL menu, 218 PRGM I/O (Input/Output) menu, 215 PRGM menu, 214 prod (product), 52, 160, 338 program editor, 214 menus and screens, 215, 220 program flow, 56 programming assembly language, 225 calling a program, 224 copying a program, 225 creating programs, 214 defined, 214 deleting a program, 223 downloading assembly programs, 225 editing a program, 223 entering a command line, 220 getting started, 214 interrupting program, 222 running program, 221 using variables, 225 Prompt (PRGM I/O menu), 216, 338

prompts, 22 Eval x=, 76 Name=, 22, 39, 76 Rcl, 42 Sto, 212 PTCHG, 105 PtChg(, 338 PTOFF, 105, 108 PtOff(, 338 PTON, 105, 108 PtOn(, 338 PwrR (power regression), 190, 339 PxChg(, 103, 340 PxOff(, 103, 340 PxOn(, 103, 340 PxTest(, 103, 340

Q Q'n equation variables, 135 Qrtl1, 193 Qrtl3, 193 Quick Zoom, 91 in parametric graphing, 129 in polar graphing, 120

Quick-Find Locator (A to Z Reference), 262

R r

(radian entry), 341 rAdd, 184 rAdd(, 340 Radian (angle mode), 35 radian angle mode, 75, 341 radian complex-number mode, 70 radian entry (r), 341 rand (random), 50, 341 randBin( (random binomial), 50, 341 randInt( (random integer), 50, 342 randM( (random matrix), 184, 342 randNorm( (random normal), 50, 342 random number, 50 RCGDB (recall graph database), 76, 88, 343 RcPic (recall picture), 76, 102, 343

99INDEX.DOC TI-86, Index, US English Bob Fedorisko Revised: 02/13/01 2:51 PM Printed: 02/27/01 1:29 PM Page 415 of 15

415

RCPIC menu, 76 REAL, 43, 175, 185, 343 4REAL (to real number), 156, 170, 179 real number variables, 43 real numbers, 29 real portion of complex number, 71 4Rec (to rectangular), 71, 174, 343 recalling variable values, 18, 42 receiving transmitted data, 241 rectangular complex mode, 35 rectangular complex numbers, 70 rectangular complex-number form, 20 rectangular graph, 84 rectangular vector coordinates, 36 RectC (rectangular complex), 35, 344 RectGC (rectangular graph coordinates), 84, 344 RectV (rectangular vector coordinate mode), 36, 344 RECV (LINK menu), 236

416

Index

RECV (LINK SND85 menu), 240 redefining user-created constants, 60 ref (row echelon form), 184, 344 regression models, 191 relational functions, 55, 56 RENAM (rename), 241 Repeat (PRGM CTL menu), 218, 345 replacing batteries, 16 resetting memory, 232 result, 20, 24 result of last expression, 26 Return (PRGM CTL menu), 219, 345 RK (Runge-Kutta) method, 133, 345 rnorm (row norm), 183, 346 ROOT, 96, 97 x‡, 346 root-finder, 211 RotL (rotate left), 69, 347 RotR (rotate right), 69, 347 round(, 49, 176, 348 row of matrix, 181

rref (reduced row echelon), 184, 348 rSwap( (row swap), 184, 348 running a program, 221

S Scatter (stat plot type), 349 Sci (scientific notation), 20, 34, 349 scrolling, 19 seed value, 50 SELCT, 112 SELECT, 77 Select(, 161, 350 selection cursor, 38 SEND (LINK menu), 236 SEND WIND screen, 238 Send(, 216, 350 separator, 70 seq( (sequence), 52, 160, 351 SeqG (sequential graphing), 84, 351 series of instructions displaying, 18 SetLE, 159 SetLEdit, 161, 351

setting graph format, 83 setting graph style, 80 Shade(, 103, 104, 352 shading pattern, 104 resolution, 104 shading patterns, 80 ShftL (shift left), 69, 353 ShftR (shift right), 69, 353 ShwSt (show string), 354 sign, 49, 354 SimulG (simultaneous graphing), 84, 354 SIMULT ENTRY menu, 208 SIMULT order screen, 208 SIMULT RESULT menu, 209 simult(, 210, 354 simultaneous equation solver, 208 sin (sine), 48, 186, 355 sin L1 (arcsine), 48, 355 sine calculating, 3 sinh (hyperbolic sine), 51, 356 sinh L1 (inverse hyperbolic sine), 51, 356

99INDEX.DOC TI-86, Index, US English Bob Fedorisko Revised: 02/13/01 2:51 PM Printed: 02/27/01 1:29 PM Page 416 of 15

SinR (sinusoidal regression), 190, 193, 357 SKIP, 241 SlpFld (slope field), 134, 358 Smart Graph, 86 drawing tools, 102 in GRAPH MATH, 95 in Graph Zoom, 94 SND85 (LINK menu), 236 solution method formats, 133 solutions drawing, 148 SOLVE, 205 solver graph, 207 Solver menu, 206 Solver ZOOM menu, 208 Solver(, 358 solving differential equations, 139 solving for unknown variable, 206 sortA, 159, 359 sortD, 159, 359 Sortx, 160, 359 Sorty, 160, 359 4Sph (to spherical), 174, 360

Index SphereV (spherical vector coordinate mode), 36, 360 square ( 2), 360 square root (‡), 7, 360 St4Eq( (string to equation), 227, 361 STAT (statistical result variables), 43 STAT CALC (Calculations) menu, 189 STAT menu, 188 Stat Plot changing on/off status, 81 setting up, 195 turning on and off, 195 STAT PLOT menu, 195 STAT PLOT status screen, 194 STAT VARS (Statistical Variables) menu, 192 statistical analysis, 188 results, 192 statistical data entering, 189 plotting, 194, 195 STGDB (store graph database), 76, 88, 361 STOa, 210

STOb, 210 Stop, 219, 362 Store, 18 store symbol, 22 store to variable (¶), 362 storing a graph display, 102 storing data, 39 storing equation coefficients, 210 storing equation results, 210 STOx, 210 STPIC (store picture), 76, 88, 362 STPIC menu, 76 StReg (store regression equation), 190, 362 string, 29 concatenating, 226 creating, 226 defined, 226 storing, 226, 227 string entry, 363 STRNG (string variables), 43 STRNG (String) menu, 227 STYLE, 77 sub( (subset of string), 227, 363 submatrix

displaying, 181 subroutines, 224 subtraction (N), 363 sum, 52, 160, 364 sum of elements of list, 52 Sx (statistical result variable), 193 syntax error, 27 syntax of function, 25 syntax of instruction, 25

T T (transpose), 367 table, 110 clearing, 114 displaying, 110 navigating, 111 setting up, 113 setup editor, 113 TABLE menu, 110 Table menus, 112 table setup editor, 113 tan (tangent), 48, 364 tan L1 (arctangent), 48, 365 tangent line drawing, 107

99INDEX.DOC TI-86, Index, US English Bob Fedorisko Revised: 02/13/01 2:51 PM Printed: 02/27/01 1:29 PM Page 417 of 15

417

tanh (hyperbolic tangent), 51, 365 tanh L1 (inverse hyperbolic tangent), 51, 365 TANLN (tangent line), 96, 99 TanLn(, 103, 107, 366 TBLST (table setup editor), 112, 113 TEST menu, 55 TEXT, 105 Text(, 366 Then, 218, 305, 306 TI-GRAPH LINK, 235 tMax, 127, 136 tMin, 127, 136 TOL (Tolerance Editor), 398 tPlot, 136 TRACE, 88 TRACE (cursor), 75 Trace (Graph menu), 367 TRACE (Solver menu), 207 trace cursor, 75, 90, 144, 205 in parametric graphing, 128 in polar graphing, 120 moving, 90, 121, 129 panning, 90 Quick Zoom, 91

418

Index

stopping and resuming, 91 tracing a function, 11 transmitting data, 234, 240 error conditions, 242 insufficient memory, 242 transmitting data (continued) repeating to several devices, 242 selecting variables, 238 window variables, 239 transpose ( T), 367 tStep, 127, 136, 138 turning off TI-86, 2, 17 turning on TI-86, 2, 17 TwoVa (TwoVar), 189, 368

U unevaluated expression storing, 9, 40 units of measure converting, 61 unit-to-unit cable, 234, 235 unitV (unit vector), 173, 368 unknown variable solving for, 206 upper menu, 32

selecting an item, 33 user-created constants, 43, 58, 60 user-created zoom variables, 239

V value, 24, 25, 29 variable, 21 classifying as data types, 42 copying, 41 creating, 39 deleting, 45 displaying, 41 in expressions, 4 in table screen, 111 names, 44 recalling, 42 storing data to, 39 storing results to, 3, 30 uppercase and lowercase names, 39 x variable, 77 y variable, 77 variable equations in a table, 114 VARS CPLX (complex variables) screen, 71

VARS EQU menu, 203 vc4li (vector to list), 160, 174, 369 vector, 29 brackets [ ], 369 complex, 171, 180 creating, 170 defined, 168 deleting from memory, 170 displaying, 171 editing dimension and elements, 172 forms, 168 operations, 173 using in an expression, 172 with math functions, 176 vector coordinate modes, 36 vector editor, 168 Vector Editor menu, 170 vector entry [ ], 369 VECTR (vector names), 43 VECTR CPLX (Complex) menu, 175 VECTR MATH menu, 173 VECTR menu, 169 VECTR NAMES menu, 169

99INDEX.DOC TI-86, Index, US English Bob Fedorisko Revised: 02/13/01 2:51 PM Printed: 02/27/01 1:29 PM Page 418 of 15

VECTR OPS (Operations) menu, 173 VERT (vertical line), 104, 106, 369

W warranty information, 400, 402 While, 218, 369 WIND (Solver menu), 206 WIND (window variables), 43, 35, 75, 238 window editor, 75 polar, 118 window variables, 82 @x and @y, 83 changing, 12, 82 differential equations, 135 graph screen, 81

X x variable, 77 XMIT (transmit), 237, 240 Xor (Boolean), 69, 370 xRes (resolution), 81 xScl (scale), 81 xStat (x-variable list), 189

Index xyline, 370

Y y variable, 77 y(x)=, 75 YICPT (y-intercept), 96, 100 yScl (scale), 81 yStat (y-variable list), 189

Z ZData, 371 ZDATA (GRAPH ZOOM menu), 92 ZDecm, 372

ZDECM (GRAPH ZOOM menu), 92 ZFACT (ZOOM FACTOR), 92, 208 ZFit, 129, 373 ZFIT (GRAPH ZOOM menu), 92 ZIn (zoom in), 373 ZIN (zoom in), 92, 208 ZInt, 374 ZINT (GRAPH ZOOM menu), 92 ZOOM, 14, 75, 88 custom, 93 parametric graphs, 129 polar graphs, 121

ZOOM operations, 147 zoom window variables storing and recalling, 95 ZOOMX (GRAPH ZOOM menu), 92 ZOOMY (GRAPH ZOOM menu), 92 ZOUT (zoom out), 92, 208, 375 ZPREV (zoom previous), 92, 375 ZRCL (GRAPH ZOOM menu), 92, 95 user-created zoom variables, 239

99INDEX.DOC TI-86, Index, US English Bob Fedorisko Revised: 02/13/01 2:51 PM Printed: 02/27/01 1:29 PM Page 419 of 15

419

ZRcl (zoom recall), 376 ZSqr, 376 ZSQR (GRAPH ZOOM menu), 92 ZSTD (GRAPH ZOOM menu), 92 ZSTD (standard defaults), 208, 377 ZSTO (GRAPH ZOOM menu), 92, 95 ZTrig, 378 ZTRIG (GRAPH ZOOM menu), 92

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TI-86 Guidebook - Mathematics | Oregon State University

TI-86 GRAPHING CALCULATOR GUIDEBOOK TI-GRAPH LINK, Calculator-Based Laboratory, CBL, CBL 2, Calculator-Based Ranger, CBR, Constant Memory, Automatic ...

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