TI86 GRAPHING CALCULATOR GUIDEBOOK
TIGRAPH LINK, CalculatorBased Laboratory, CBL, CBL 2, CalculatorBased 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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Table of Contents TI86 Quick Start
1
Preparing to Use Your New TI86 ..................................................... 2 Installing the AAA Batteries ......................................................... 2 Turning On and Turning Off the TI86.......................................... 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 Reevaluating 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 TI86
15
Installing or Replacing Batteries .....................................................16 When to Replace Batteries .........................................................16 Turning On and Turning Off the TI86.............................................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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TI86 Table of Contents
The ALPHA Key........................................................................... 21 ALPHAlock and alphalock........................................................ 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 TI86 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 CATLGVARS (CATALOGVariables) 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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TI86 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 BuiltIn and UserCreated Constants..................................... 58 The CONS (Constants) Menu...................................................... 58 The CONS BLTIN (BuiltIn Constants) Menu............................... 58
v
Creating or Redefining a UserCreated 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 ÕÚ (Hexadecimal Characters) Menu .........................67 Entering Hexadecimal Digits.......................................................67 The BASE TYPE Menu.................................................................67
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TI86 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 TI86 ................................................................88 The GRAPH Menu.......................................................................88 Using the FreeMoving 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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TI86 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 FreeMoving 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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TI86 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 FreeMoving 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 BuiltIn Variable fldPic .......................................................138 Displaying the Graph................................................................138 Entering and Solving Differential Equations..................................139 Graphing in SlpFld Format........................................................139 Transforming an Equation into a FirstOrder 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 FreeMoving 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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TI86 Table of Contents
Chapter 11: Lists
151
Lists on the TI86 .......................................................................... 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 AttachedFormula 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 TI86 .....................................................................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 TI86....................................................................178 Creating, Storing, and Displaying Matrices ...................................178
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TI86 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 TI86.................................................... 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 EquationEntry Editor........................203 Setting Up the InteractiveSolver 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 RootFinder ..........................................................211
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TI86 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 TI86 .................................................... 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 TI86 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 TI86 .......................................................................232 The MEM RESET (Reset) Menu.................................................232 ClrEnt (Clear Entry)...................................................................232
Chapter 18: The TI86 Communication Link
233
TI86 Linking Options....................................................................234 Linking Two TI86s ...................................................................234 Linking a TI86 and a TI85......................................................234 Linking a TI86 and a CBL 2/CBL or CBR System......................234 Linking a TI86 and a PC or Macintosh ....................................235 Downloading Programs from the Internet................................235 Connecting the TI86 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 TI85 ....................................................239
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TI86 Table of Contents
The LINK SND85 (Send Data to TI85) 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 PredatorPrey Model ..................................................................... 258 Program: Sierpinski Triangle ......................................................... 260
Chapter 20: A to Z Function and Instruction Reference
Appendix
379
TI86 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
QuickFind Locator........................................................................ 262 Alphabetical Listing of Operations................................................ 266
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TI86 Quick Start TI86
Preparing to Use Your New TI86 ........................................ 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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Quick Start
Preparing to Use Your New TI86 The brief examples in the TI86 Quick Start demonstrate some common TI86 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 TI86 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 TI86 turns off automatically.
Turning On and Turning Off the TI86 To turn on the TI86, press ^, which is in the bottomleft corner of the keyboard. You should see the entry cursor ( Å ) blinking in the topleft 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 TI86, press  . 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 halfshaded 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
xVAR
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 integerpart examples). Otherwise, the screens your TI86 shows may differ from the screens pictured next to the activities. Calculating the Sine of a Number
The TI86 onscreen 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 TI86 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 TI86 automatically pasted Ans before ¶. (continued)
(:) X
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Quick Start
When ALPHAlock 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. ALPHAlock 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 TI86, { 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.)
Œ
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 ( Œ &).
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 Reevaluating the Previous Entry When you press b, the TI86 stores the expression or instruction you entered to the builtin 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 TI86 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 TI86.
Enter the builtin 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 TI86 plots four types of functions on the graph screen. To plot a graph, you must store an unevaluated expression to a builtin 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 yaxes 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 freemoving cursor ( + ) around the graph screen. The cursor coordinates are displayed at the bottom of the graph.
"#!$
freemoving 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 topright corner.
)
Move the trace cursor from the function y1 to the function y2. The 1 in the topright corner changes to 2; the y value changes to the value of y2 at x=0. (continued)
$
trace cursor
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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 TI86 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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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 zoombox cursor.
&
Move the zoombox 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 TI86 TI86
Installing or Replacing Batteries ........................................ 16 Turning On and Turning Off the TI86 ............................... 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 TI86 Menus ............................................................ 31 Viewing and Changing Modes........................................... 34
M1
M2
M3
M4
M5
F1
F2
F3
F4
F5
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Chapter 1: Operating the TI86
Installing or Replacing Batteries Your new TI86 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  ) 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 TI86 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 lowbattery message is displayed as you turn on the calculator. Generally, the calculator will continue to operate for one or two weeks after the lowbattery message is first displayed. Eventually, the TI86 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 TI86 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 TI86 To turn on the TI86, press ^. ♦ If you previously had turned off the calculator by pressing  , the TI86 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 TI86 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 TI86 manually, press  . All settings and memory contents are retained by the Constant Memory TM feature. Any error condition is cleared. APD turns off the TI86 automatically after about four minutes of nonuse 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 halfshaded 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
xVAR
MORE x
INS
DEL
18
Chapter 1: Operating the TI86
The TI86 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 topright 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 lowbattery message is displayed.
The Home Screen When you first turn on your TI86, the home screen is displayed. Initially, the home screen is a blank screen, except for the entry cursor ( Å ) in the topleft 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 reexecute previous entries, use  ¢ (page 28).
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Chapter 1: Operating the TI86 The mode settings control the way the TI86 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 TI86 onscreen 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 numberentry 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 TI86 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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Chapter 1: Operating the TI86
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 threedigit 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 engineeringnotation numbers in an expression, the TI86 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 TI86, the complex number a+bi is entered as (a,b) in rectangular complexnumber form or as (rq ) in polar complexnumber 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
xVAR
MORE x
INS
DEL
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Chapter 1: Operating the TI86
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 ALPHAlock automatically.
 š returns the STAT menu
STAT
X
STAT
X
STAT
21
X
1 ãXä returns an X
 n ãXä returns an x
ALPHAlock and alphalock To enter more than one uppercase or lowercase alpha character consecutively, set ALPHAlock (for uppercase letters) or alphalock (for lowercase letters). To set ALPHAlock when the entry cursor is displayed, press 1 1. ♦ To cancel ALPHAlock, press 1. ♦ To switch from ALPHAlock to alphalock, press  n. To set alphalock when the entry cursor is displayed, press  n 1. ♦ To cancel alphalock, press 1 1.
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Chapter 1: Operating the TI86
♦
To switch from alphalock to ALPHAlock, press 1.
You can use  when ALPHAlock or alphalock 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 TI86
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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Chapter 1: Operating the TI86
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 TI86, 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 TI86 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 orderofevaluation 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 TI86
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 TI86 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 TI86. 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 builtin function or instruction typically is easier.
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Chapter 1: Operating the TI86
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 TI86 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 TI86 is calculating or graphing, a moving vertical line is displayed as the busy indicator in the topright 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 TI86
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 nongraphing 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 TI86 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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Chapter 1: Operating the TI86
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 TI86, 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
Reexecute the edited entry.
b
Retrieving Previous Entries The TI86 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 TI86
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 reentry.
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 TI86 stores the answer to a builtin variable called Ans (last answer). Ans may be a real or complex number, list, vector, matrix, or string. When you turn off the TI86, the value in Ans is retained in memory.
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Chapter 1: Operating the TI86
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 TI86 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 TI86 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 TI86
31
Using TI86 Menus The symbols for many TI86 features are found in menus instead of on the TI86 keyboard. Displaying a Menu The way to display a particular menu depends on the menu’s location on the TI86.
Some TI86 menus have as many as 25 items.
MenuDisplaying Method
Example
Press a key that has a menu name on it
6 displays the GRAPH menu
Press  and then a 2ndkey menu name
 Œ displays the MATH menu
Select a menu name from another menu
 Œ & 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  Œ to 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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Chapter 1: Operating the TI86
The Menu Keys
The Appendix Menu Map shows every TI86 menu. Typically, a TI86 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 TI86
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 TI86
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 TI86 displays and interprets numbers and graphs. The Constant Memory feature retains current mode settings when the TI86 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 TI86
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 complexnumber results as (real,imaginary)
PolarC
(polar complex mode) Displays complexnumber 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 Nondecimal 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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Chapter 1: Operating the TI86
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 twoelement vectors and ãx y zä for threeelement vectors
(cylindrical vector coordinates) Displays results in the form ãr ±qä for twoelement vectors and ãr ±q zä for threeelement vectors (spherical vector coordinates) Displays results in the form ãr ± qä for twoelement vectors and ãr ±q ±fä for threeelement 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 TI86
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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Chapter 2: The CATALOG, Variables, and Characters
The CATALOG The CATALOG is the first item on the CATLGVARS menu.
w&
The CATALOG displays all TI86 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; ALPHAlock 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 TI86, 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 TI86 settings or reset defaults and memory to the factory settings. ♦ Execute functions that cause the TI86 to store data automatically to builtin variables. The TI86 has builtin 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 usercreated variable name, follow these guidelines. ♦ The usercreated 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 usercreated variable name cannot replicate a TI86 feature symbol or builtin variable. For example, you cannot create abs, because abs is the absolute value function symbol. You cannot create Ans, because it is already a builtin variable name. ♦ The TI86 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 builtin variable name; ANS and ans can be usercreated variable names.
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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. ALPHAlock 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 TI86 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 usercreated variable or to a valid builtin 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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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. ALPHAlock 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 TI86 recognizes the data type according to the editor. For example, only vectors are stored using the vector editor.
The TI86 classifies variables according to data type and places each variable on a datatype selection screen. You can display each screen by selecting the appropriate data type from the CATLGVARS menu, as described on page 43. Here are some examples. If data...
The TI86 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 CATLGVARS (CATALOGVariables) 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 userdefined 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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Chapter 2: The CATALOG, Variables, and Characters
Selecting a Variable Name The example assumes that the realnumber variables AREA and VOL from the example on page 41 have not been deleted from memory.
Select the appropriate datatype selection screen from the CATLGVARS 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. ALPHAlock 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 TI86 builtin 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 usercreated variable name (except a program name) and its contents, the syntax is: DelVar(variable) To delete usercreated 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
Ÿ
INTL
miscellaneous international characters characters menu menu Greek characters menu
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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 variablename characters, including the first letter. p (  ~ ) is not valid as a character; p is a constant on the TI86.
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. ALPHAlock is on. If necessary, switch to alphalock.
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 TI86
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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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 elementbyelement 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 TI86 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
Œ HYP
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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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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The InterpolateàExtrapolate Editor  Œ / & Using the interpolateàextrapolate editor, you can interpolate or extrapolate a value linearly, given two known pairs and the xvalue or yvalue 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 usercreated variable, to builtin 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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The builtin variable d defines the step size in calculating nDer( (in dxNDer differentiation mode only) and arc(. The builtin 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 TI86 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 TI86 performs the addition first, and then compares 4 to 5. ♦ The expression 2+(2==2)+3 evaluates to 6. The TI86 performs the test in parentheses first, and then adds 2, 1, and 3.
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Constants, Conversions, Bases, and Complex Numbers TI86
Using BuiltIn and UserCreated 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 BuiltIn and UserCreated Constants A constant is a variable with a specific value stored to it. The CONS BLTIN menu items are common constants built into the TI86. You cannot edit the value of a builtin constant. You can create your own constants and add them to the usercreated constant menu for easy access. To enter a usercreated constant, you must use the usercreated constant editor (page 60); you cannot use X or = to create a constant. ‘
The CONS (Constants) Menu BLTIN
EDIT
USER
builtin usercreated constants menu constants menu usercreated constants editor
The CONS BLTIN (BuiltIn Constants) Menu You can select builtin 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.
BuiltIn 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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Chapter 4: Constants, Conversions, Bases, and Complex Numbers
Creating or Redefining a UserCreated 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. ALPHAlock 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 usercreated 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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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 usercreated 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 TI86, 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 unitofmeasure 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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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 TI86 order of evaluation will perform the conversion first, and then apply the negation to the converted value. If you enter...
...The TI86 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 ltyr
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 lightyears
¡F
’*
degrees Fahrenheit
¡K degrees Kelvin
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¡R degrees Rankin
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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
’/)
ftlb footpounds kwhr kilowatt hours eV electron Volts
erg latm
ergs literatmospheres
’/* ftlbàs calàs
footpounds 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 TI86 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 TI86 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 TI86 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 ÕÚ
TYPE
CONV
— BOOL
BIT
hexadecimal base conversion rotateàshift characters menu menu menu base type Boolean operator menu menu
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Chapter 4: Constants, Conversions, Bases, and Complex Numbers BASE ÕÚ 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 ÕÚ (Hexadecimal Characters) Menu
—&
This is the BASE ÕÚ 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 /...
{ ÕÖ
} ×
NAMES Ø
" Ù
OPS Ú
4
{ Õ
} Ö
NAMES ×
" Ø
OPS ÙÚ
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 ÕÚ 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 ÕÚ 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 ÕÚ 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.
ÕÚ 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 TI86, 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
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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 (nonreal) 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 TI86 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 TI86
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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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 TI86 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
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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 TI86 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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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 TI86 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 nonreal number, the value is not plotted on the graph; no error is returned.
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Chapter 5: Function Graphing
The TI86 graphs all selected functions on the same graph screen.
79
Selecting Graph Styles Depending on which graphing mode is set, the TI86 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.
Â (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 TI86 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
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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 TI86 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 xaxis. yScl (y scale) is the number of units represented by the distance from one tick mark to the next tick mark on the yaxis. 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 xaxis. ♦ At xRes=8, functions are evaluated and graphed at every eighth pixel along the xaxis.
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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
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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 TI86 automatically recalculates xMax and yMax from @x, xMin, @y, and yMin, and the new values are stored.
Setting the Graph Format The TI86 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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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 freemoving 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 freemoving 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 topright corner as the TI86 draws the graph. ♦ In SeqG format, the TI86 draws each selected function one by one, in functionname order (for example, y1 is graphed first, y2 is graphed second, and so on). ♦ In SimulG format, the TI86 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 topright 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)
:
Freemoving cursor and coordinate values but not the menus
b
Cursor and coordinate values but not the menus
6 or GRAPH
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Chapter 5: Function Graphing
Graphing a Family of Curves If you enter a list as an element in an equation, the TI86 plots the function for each value in the list, graphing a family of curves. In SimulG graphing order mode, the TI86 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 TI86
Graph Tools on the TI86................................................... 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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Chapter 6: Graph Tools
Graph Tools on the TI86 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 24x is graphed.
The numeric display mode settings do not affect coordinate display.
89
Using the FreeMoving Cursor When you select GRAPH from the GRAPH menu, the graph screen is displayed with the freemoving 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 freemoving cursor coordinates represent the cursor location on the graph screen. Moving the freemoving 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 24x 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 independentvariable 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 TI86 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 freemoving 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 TI86 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
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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 equalsize pixels on the xaxis and yaxis; 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 builtin 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 userdefined zoomwindow 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 userdefined zoomwindow variables (ZRCL)
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Chapter 6: Graph Tools
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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 TI86 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 TI86 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 zoomwindow variables resume their standard default values when you reset defaults.
Storing and Recalling ZoomWindow Variable Values ♦ To store all current zoomwindow variable values simultaneously as a userdefined custom zoom feature, select ZSTO from the GRAPH ZOOM menu. ♦ To execute a userdefined custom zoom, which resets the graph screen to the stored zoomwindow variables, select ZRCL from the GRAPH ZOOM menu. Using ZSTO in these graphing modes: Stores to these zoomwindow 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 TI86 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 yintercept (y at x=0)
ISECT
Finds the intersection of two functions using a specified left bound, right bound, and guess
DIST
Finds the straightline 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 stepsize variable d (Appendix) affects the accuracy of dyàdx, INFLC in dxNDer differentiation mode (Chapter 1), ARC, and TANLN. Accuracy increases as the stepsize 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
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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
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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 yintercept, the cursor coordinate values are displayed, and y is stored in Ans.
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Chapter 6: Graph Tools
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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 bottomleft 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 topright 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 ycoordinate 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 0row62 and 0column126. 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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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 yaxis and its y values on the xaxis. 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 alphalock and enter min. (The alpha cursor ( Ï ) is displayed in the topright corner.
n1 ãMä ãIä ãNä
Move the cursor to another location.
ãMä ãAä ãXä
Enter max (alphalock 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 TI86
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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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+3x4 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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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 +3x4 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 TI86
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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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 TI86 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 TI86 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 TI86 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 FreeMoving Cursor The freemoving 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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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
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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 bottomleft 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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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 ycoordinates of the graph screen. DrInv is not available in Pol graphing mode.
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9
Parametric Graphing TI86
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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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 ` 8F2eI # 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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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 TI86 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 Funcmode 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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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 TI86 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 TI86 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 FreeMoving Cursor The freemoving 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 bottomleft 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 ycoordinate values of the graph screen.
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10
Differential Equation Graphing TI86
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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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 firstorder 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 TI86 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 TI86 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 freemoving 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 RungeKutta 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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Chapter 10: Differential Equation Graphing
Field Format SlpFld
(slope field) Adds the slope field to the graph of only one firstorder equation with t on the xaxis and a specified Qn equation on the yaxis
DirFld
(direction field) Adds the direction field to the graph of only one secondorder equation with Qx# on the xaxis and Qy# on the yaxis
FldOff
(field off) Graphs all selected differential equations with t or Q1 on the xaxis, Q1 or Q2 on the yaxis, 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 firstorder 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 TI86 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 TI86 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 TI86 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 Â (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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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 firstorder 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 TI86 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
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Setting the Axes To display the axes editor, select AXES from the GRAPH menu in DifEq mode (6 )). x= assigns a variable to the xaxis dTime= specifies a point in time (real number) y= assigns a variable to the yaxis 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 secondorder 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 xaxis 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 TI86 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 TI86 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 BuiltIn Variable fldPic As the TI86 plots a field, it stores the field and any displayed label, axes, or cursor coordinate information to the builtin 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 ♦ Reassigning 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 TI86 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 23) determines the step size. If the xaxis 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 TI86, 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 firstorder 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 FirstOrder System On the TI86, to enter a secondorder or higher (up to ninthorder) differential equation, you must transform it to a system of firstorder differential equations. For example, to enter the secondorder differential equation y''= L y, you must transform it to two firstorder 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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Chapter 10: Differential Equation Graphing
Graphing a System of Equations in FldOff Format For this example, you must transform the fourthorder differential equation y (4)Ny=e Lx into an equivalent system of firstorder 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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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 TI86 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 FreeMoving Cursor The freemoving 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 yaxis 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 bottomleft 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 ycoordinates 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 freemoving 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 yaxes.
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 freemoving 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 ALPHAlock is on for ãYä and ãNä only. ♦ To use DrEqu( again with new initial conditions, press ãYä, ", #, !, or $. ♦ To leave DrEqu( and display the GRAPH menu, press ãNä or ..
Using ZOOM Operations The GRAPH ZOOM menu items, except ZFIT, work the same in DifEq graphing mode as in Func graphing mode. In DifEq graphing mode, ZFIT adjusts the graph screen in both the x direction and y direction. The ZOOM menu items affect only the x (xMin, xMax, and xScl) and y (yMin, yMax, and yScl) window variables. The t window variables (tMin, tMax, tStep, and tPlot) are not affected, except with ZSTD and ZRCL. You may want to edit the t window variables to ensure that sufficient points are plotted. ZSTD sets difTol=.001 and t and Q as the axes.
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Chapter 10: Differential Equation Graphing
Drawing Solutions Interactively with EXPLR
Display the mode screen and set DifEq graphing mode.
m### #"""b
Display the format screen and set FldOff field format.
6/&# ####"" b
Display the equation editor and store the equation Q'1=.001Q1(100NQ1). (Delete all other equations.)
& ` 001 ' 1 D 100 T ' 1 E
Set the axes to x=t and y=Q1.
h#"1
Display the window editor and set the window variable values.
 f # 100 # `2### 100 # # # 110
Display the initial conditions editor and enter the initial condition.
( 10
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Chapter 10: Differential Equation Graphing
Select EXPLR from the GRAPH menu.
/*
Move the freemoving cursor to the initial condition for which you want to solve.
"#!$
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 freemoving 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, tMinttMax. 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 TI86
Lists on the TI86............................................................. 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 TI86 The length and number of lists you can store in the TI86 is limited only by memory capacity.
A list is a set of real or complex elements, as in {5,L20,13,9}. On the TI86, 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 CalculatorBased Laboratory™ (CBL 2™/CBL™) or CalculatorBased Ranger™ (CBR) and store it to a list name on the TI86 (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 TI86, 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 usercreated 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. ALPHAlock 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 TI86 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
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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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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. ALPHAlock 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 editelement 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 usercreated 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 TI86 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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Chapter 11: Lists
The list editor displays a formulalock symbol next to each list name that has a formula attached to it.
Attach the formula and generate the list. The TI86 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 AttachedFormula Lists When you edit an element of a list referenced in an attached formula, the TI86 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 attachedformula list also is displayed, the TI86 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 attachedformula 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 attachedformula 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 attachedformula 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 attachedformula list element. ♦ Use ""¶listName, where listName is the attachedformula list. ♦ In the list editor, move the cursor onto the name of the attachedformula 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 attachedformula 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 AttachedFormula List As described above, one way to detach a formula from a list name is to edit an element of the attachedformula list. The TI86 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 attachedformula list. The protection feature prevents you from deleting an element of an attachedformula list. To delete an element of a attachedformula list, you must first detach the formula in any of the ways described above.
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12
Vectors TI86
Vectors on the TI86 ........................................................ 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 TI86 A vector is a onedimensional 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 TI86 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 TI86 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 TI86, you can store up to 255 elements to a vector in rectangular form. You can use two or threeelement vectors to define magnitude and direction in a two or threedimensional space. You can express two or threeelement vectors in different forms, depending on the type of vector. To express a...
You enter:
And the TI86 returns:
Twoelement rectangular vector
ãx,yä
ãx yä
Twoelement cylindrical vector
ãr±qä
ãr±qä
Twoelement spherical vector
ãr±qä
ãr±qä
Threeelement rectangular vector
ãx,y,zä
ãx y zä
Threeelement cylindrical vector
ãr±q,zä
ãr±q zä
Threeelement 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 TI86 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'
ALPHAlock 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 TI86 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 threeelement 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 twoelement or threeelement 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 threeelement vector conversion equations for cylindrical form ãr q zä are: x = r cosq y = r sinq z=z The threeelement 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 2element vector in polar form ãr±qä
vector4Cyl
Displays a 2 or 3element vector as a cylindrical vector ãr±q 0ä or ãr±q zä
vector4Sph
Displays a 2 or 3element vector as a spherical vector ãr±q 0ä or ãr±q fä
complexVector4Rec
Displays a 2 or 3element 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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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 TI86
Matrices on the TI86 ...................................................... 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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Chapter 13: Matrices
Matrices on the TI86 A matrix is a twodimensional 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 TI86 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.
‰'
ALPHAlock 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 topright corner of the screen, (1row255 and 1column255); 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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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.
Xn 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 TI86 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 (lowerupper) 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 rowechelon form of matrix
rref matrix
Returns the reduced rowechelon 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 TI86
Statistical Analysis on the TI86 ...................................... 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 TI86 With the TI86, you can analyze onevariable and twovariable statistical data, which are stored in lists. Onevariable data has one measured variable. Twovariable 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
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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 TI86 has three builtin list names for statistics, xStat (xvariable list), yStat (yvariable list), and fStat (frequency list). TI86 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 xlist used in the last statistical analysis
yStat
An automatically updated list of the data from the ylist 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
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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 (yintercept) (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 xlist and ylist 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 leastsquares fit.
d P2Reg
(quadratic regression) Fits the seconddegree 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 thirddegree 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 fourthdegree 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 twovariable 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
1Var Stats
2Var Stats
mean of x values
v
v
correlation coeff
corr
sx
sx
yintercept 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
1Var Stats
2Var 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 (yint) 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 TI86 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
Plottype icon
® xStat
Independent list name
yStat
›
Marktype 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=
independentdata list name
xStat
LIST NAMES menu
Ylist Name=
dependentdata 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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Chapter 14: Statistics
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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 onevariable 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 onevariable 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 onevariable 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
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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 TI86 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 onevariable 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 xvalue or yvalue 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 TI86
Preview: The Equation Solver .......................................... 202 Entering an Equation in the EquationEntry Editor .......... 203 Setting Up the InteractiveSolver Editor........................... 204 Solving for the Unknown Variable ................................... 206 Graphing the Solution...................................................... 207 Solver Graph Tools........................................................... 207 The Simultaneous Equation Solver .................................. 208 The Polynomial RootFinder............................................. 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 equationentry 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 interactivesolver 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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Chapter 15: Equation Solving
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Entering an Equation in the EquationEntry Editor The equation solver uses two editors: the equationentry editor, where you enter and edit the equation you want to solve, and the interactivesolver 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 equationentry 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 TI86 automatically stores it to the variable eqn.
You can display other menus in the equationentry 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 TI86 automatically converts it to the equation exp=equationVariable. If you enter an expression directly, the TI86 automatically converts the expression to the equation exp=expression.
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Setting Up the InteractiveSolver Editor In the example, the equation V1=V(R1à(R1+R2)) was entered in the equationentry editor. If you entered an expression for eqn, then exp= is the first variable prompt on the interactivesolver editor.
After you have stored an equation to eqn in the equationentry editor, press b to display the interactivesolver 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 interactivesolver 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 interactivesolver editor, the default bound={L1E99,1E99} is displayed. These are the maximum bounds for the TI86.
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The TI86 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 TI86 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 twoelement 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 TI86 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 freemoving 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 interactivesolver editor. Editing the Equation To edit the equation stored to eqn when the interactivesolver editor is displayed, press $ until the cursor is on the equation. The equationentry editor is displayed. The TI86 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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The Solver Menu You can display other menus in the interactivesolver editor
GRAPH
WIND
 t equation b ZOOM
TRACE SOLVE
graphs the solver zoom solves for the unknown variable or menu displays the interactivesolver 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 interactivesolver 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 freemoving 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 xaxis. 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 freemoving cursor or trace cursor to select a guess on the graph.
You can explore the graph of a solution with the freemoving cursor, as you would on any other graph. When you do, the coordinate values for the variable (the xaxis) and the value leftNrt (the yaxis) 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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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 coefficientsentry 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 coefficientsentry 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 coefficientsentry screen, if possible.
Display the coefficientsentry 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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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 coefficientsentry 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. ALPHAlock 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 coefficientsentry 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 RootFinder
v
The root finder solves up to 30thorder real or complex polynomials. Entering and Solving a Polynomial The POLY coefficients are not variables. You can display other menus in the coefficientsentry editor.
Display the POLY order screen.
v
Enter an integer between 2 and 30. The coefficientsentry 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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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. ALPHAlock 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. ALPHAlock 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 coefficientsentry screen, where you can edit coefficients and calculate new solutions, select COEFS from the POLY RESULT menu.
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Programming TI86
Writing a Program on the TI86 ....................................... 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 TI86 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 TI86 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 TI86 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. ALPHAlock 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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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 TI86 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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Input
Displays the current graph and lets you use the freemoving 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 TI86, you can use Input to receive variable from a CBL 2/CBL, CBR, or TI86 (TI85 compatible)
For Input and Prompt, builtin 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 TI86 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 TI86, you can use Outpt( to send listName to a CBL 2/CBL or CBR (for TI85 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 TI86 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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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 builtin 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 builtin 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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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 = Â (dotted)
*LCust(item#,"title" ã,item#,"title",...ä)
Loads (defines) the TI86 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 TI86 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 programonly 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 lastanswer variable Ans (Chapter 1). The TI86 reports errors as the program runs. Commands executed during a program do not update the previousentry storage area ENTRY (Chapter 1). The example program below is shown as it would appear on a TI86 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 TI86, 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 TIcreated assembly language programs to add features to your TI86 that are not built in. For example, you can download the TI83 finance or inferential statistics features to use on your TI86.
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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 TI86 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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Chapter 16: Programming
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 TI86
Checking Available Memory ............................................ 230 Deleting Items from Memory ........................................... 231 Resetting the TI86 .......................................................... 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
checkRAM 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 TI86 has 98,224 bytes of available randomaccess 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 50byte 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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231
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 usercreated 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; ALPHAlock is on.
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Chapter 17: Memory Management
Resetting the TI86 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 TI86 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 TI86 Communication Link TI86
TI86 Linking Options ...................................................... 234 Connecting the TI86 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 TI86 Communication Link
TI86 Linking Options Using the unittounit cable included with the TI86, you can transmit data between the TI86 and several other devices. Linking Two TI86s You can link two TI86 units and select the data types to be transmitted, including programs. You can back up the entire memory of a TI86 onto another TI86. Linking a TI86 and a TI85 You can select the data types, including programs, to transfer from a TI85 to a TI86. You can send most variables and programs from a TI86 to a TI85 using SND85 (page 239), except lists, vectors, or matrices that exceed TI85 capacity. When you run a TI85 program on a TI86, the TI85 PrtScrn program instruction is not valid. Also, the EOS implied multiplication on the TI86 differs from the TI85 (Appendix). For example, the TI85 interprets sin 2x as sin (2x); the TI86 interprets sin 2x as (sin 2)x. Linking a TI86 and a CBL 2/CBL or CBR System The CalculatorBased Laboratoryé (CBL 2é/CBLé) and CalculatorBased 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 TI86 and analyze. You can transmit list names to a CBL 2/CBL or CBR from a TI86.
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Linking a TI86 and a PC or Macintosh TI86 TIGRAPH LINKè is an optional system that links a TI86 with an IBMêcompatible or Macintoshê computer. Downloading Programs from the Internet If you have TIGRAPH 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 TI83 finance and inferential statistics. The site also links to many other TI86 web sites maintained by user groups, high schools, universities, and individuals.
Connecting the TI86 to Another Device Before you begin to transmit data to or from the TI86, connect it to the other device.
Firmly insert one end of the unittounit 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 TI86 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 TI85 receive mode (waiting)
Selecting Data to Send The CBL 2/CBL, CBR, and TI86 TIGRAPH LINK have builtin 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
usercreated constants pictures
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EQU
Chapter 18: The TI86 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 receivingcalculator 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 receivingcalculator memory with the backup data. ♦ To cancel backup and retain all receivingcalculator 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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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 graphscreen data for that TI86 graphing mode and for ZRCL (usercreated 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 usercreated 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 TI85 The steps for selecting variables to send to a TI85 are the same as those for selecting variables to send to a TI86. However, the LINK SND85 menu has fewer items than the LINK SEND menu. The TI86 has more capacity for lists, vectors, and matrices than the TI85. If you send to the TI85 a list, vector, or matrix that has more elements than the TI85 allows, the elements that exceed TI85 capacity are truncated. The LINK SND85 (Send Data to TI85) Menu MATRX
LIST
VECTR
REAL
CPLX
o( 4
CONS
PIC
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STRNG
240
Chapter 18: The TI86 Communication Link
Preparing the Receiving Device To prepare a PC to receive data, consult the TIGRAPH LINK guidebook.
To prepare a TI86 or TI85 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 TI86 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 TI86 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 TI86 without having to reselect data. To repeat a transmission with another device, disconnect the unittounit 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 TI86 and a TI85. 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 TI86
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 PredatorPrey 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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Chapter 19: Applications
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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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Chapter 19: Applications
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 TI86, 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 xaxis and CURR on the yaxis.
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xRes=4
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 yaxis).
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.
쐅
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.
쐈
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).
쐉
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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Chapter 19: Applications
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 higherorder 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): 202210.
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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Chapter 19: Applications
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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xRes=4
Chapter 19: Applications
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Next, use the list editor and a degreethree 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.
쐅
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.
쐉
In the equation editor, enter the apparent characteristic polynomial of matrix A and select ¼ (thick) graph style as shown. ¼y3=Lx^3+14xN24
씈
Graph y1, y2, y3, and Plot1.
씉
Deselect y2 in the equation editor.
씊
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 closedform 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 TI86 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 TI86, 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 valvesize and valvetype 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 builtin acceleration of gravity constant When you graph these equations on the TI86, the yaxis (x=0) is the side of the reservoir where the valve is to be installed. The xaxis (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 :.
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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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PredatorPrey Model The growth rates of predator and prey populations, such as foxes and rabbits, depend upon the populations of both species. This initialvalue problem is a form of the predatorprey 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 phaseplane 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 phaseplane solution.
To see a family of specific phaseplane 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}
쐅
Select TRACE from the GRAPH menu to display the graph with the trace cursor.
쐈
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 phaseplane 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 TI86
QuickFind Locator........................................................... 262 Alphabetical Listing of Operations................................... 266
M1
M2
M3
M4
M5
F1
F2
F3
F4
F5
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QuickFind Locator This section lists the TI86 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. Nonalphabetic 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 TI86 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 builtin equation variables used for graphing are casesensitive. 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 builtin 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 wellbehaved squareMatrix is expected to be for certain matrix functions, particularly inverse. For a wellbehaved matrix, the condition number is close to 1. log(cond squareMatrix) indicates the number of digits
that may be lost due to roundoff 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 CayleyHamilton 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 2D vector is treated as a 3D 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 3element real vector result in cylindrical form, [rq z], even if the display mode is not set for cylindrical (CylV).
VECTR OPS menu
CylV
CylV
Sets cylindrical vector coordinate mode ( [rq 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 [23.14159265359 0] [L2,0,1]4Cyl b [23.14159265359 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 usercreated 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 builtin 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]]
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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 casesensitive. 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 casesensitive. 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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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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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 lastdrawn 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 yaxis and y values on the xaxis.
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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Done 0
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Chapter 20: A to Z Function and Instruction Reference
DS<( ‡ program editor CTL menu
:DS<(variable,value) :commandifvariable‚value :commands
Decrements variable by 1. If the result is < value, skips commandifvariable‚value. If the result is ‚ value, then commandifvariable‚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 builtin 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. TI86 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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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 IfThen
‡ program editor CTL menu
Eng † mode screen
Else loop. Eng
In Eng notation mode:
Sets engineering notation mode, in which the powerof10 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 casesensitive.
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 builtin equation variables y1 and y2 are casesensitive: y1=x^3+x+5 b y2=2 x b eval 5 b
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Chapter 20: A to Z Function and Instruction Reference
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
Builtin equation variables such as y1, r1, and xt1 are casesensitive. 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 builtin 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 builtin variables xStat, yStat, and fStat, respectively. The regression equation is stored also to builtin 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 builtin 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 noninteger, where 0 integer 449 and 0 noninteger 449.9. For a noninteger, 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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720 1710542068.32
{720 5040 40320}
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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Done .50000000000 Done .5
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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 builtin 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 builtin 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 builtin 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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Chapter 20: A to Z Function and Instruction Reference
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 TI86 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 TI86 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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Chapter 20: A to Z Function and Instruction Reference
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 AF menu. Do not use 1 to type a letter.
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23ß
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 builtin 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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Chapter 20: A to Z Function and Instruction Reference
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 independentvariable 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 :commandiftrue :commands
If condition is true, executes commandiftrue. Otherwise, skips commandiftrue. 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 :commandsiftrue :End :commands
If condition is true (nonzero), executes commandsiftrue from Then to End. Otherwise, skips commandsiftrue 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 :commandsiftrue :Else :commandsiffalse :End :commands
If condition is true (nonzero), executes commandsiftrue 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 commandsiffalse 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 freemoving 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 noninteger, 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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L24] [[1 [L99 47 ]]
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
ƒ
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) :commandifvariablevalue :commands
Increments variable by 1. If the result is > value, skips commandifvariablevalue. If the result is value, then commandifvariablevalue 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 builtin variable.
LabelOff † graph format screen
LabelOn † graph format screen
LabelOff
Turns off axes labels. LabelOn
Turns on axes labels.
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L23] [[1 [L99 47 ]]
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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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
20 b
0
88123 b
1
L5L5 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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LgstR STAT CALC menu Builtin equation variables such as y1, r1, and xt1 are casesensitive. Do not use Y1, R1, and XT1. LgstR returns a tolMet value that indicates if the result meets the TI86’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 builtin equation variable such as y1, r1, and xt1. The equation’s coefficients always are stored as a list to builtin 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 builtin variables xStat, yStat, and fStat, respectively. The regression equation is stored also to builtin 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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Chapter 20: A to Z Function and Instruction Reference LgstR [iterations,]equationVariable
Uses xStat, yStat, and fStat for xList, yList, and frequencyList, respectively. These builtin 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
Builtin equation variables such as y1, r1, and xt1 are casesensitive. 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 builtin 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 builtin variables xStat, yStat, and fStat, respectively. The regression equation is stored also to builtin 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 builtin 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 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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LnR STAT CALC menu
Builtin equation variables such as y1, r1, and xt1 are casesensitive. 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 builtin 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 builtin variables xStat, yStat, and fStat, respectively. The regression equation is stored also to builtin 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 builtin 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 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 (lowerupper) 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 rowbyrow 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 builtin 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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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
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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 16bit 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
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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 casesensitive.
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 onevariable 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 builtin 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 builtin 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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Chapter 20: A to Z Function and Instruction Reference
P2Reg STAT CALC menu
Builtin equation variables such as y1, r1, and xt1 are casesensitive. 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 builtin equation variable such as y1, r1, and xt1. The equation’s coefficients always are stored as a list to builtin variable PRegC. Values used for xList, yList, and frequencyList are stored automatically to builtin variables xStat, yStat, and fStat, respectively. The regression equation is stored also to builtin 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 builtin 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
Builtin equation variables such as y1, r1, and xt1 are casesensitive. 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 builtin equation variable such as y1, r1, and xt1. The equation’s coefficients always are stored as a list to builtin variable PRegC. Values used for xList, yList, and frequencyList are stored automatically to builtin variables xStat, yStat, and fStat, respectively. The regression equation is stored also to builtin 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 builtin 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
Builtin equation variables such as y1, r1, and xt1 are casesensitive. 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 builtin equation variable such as y1, r1, and xt1. The equation’s coefficients always are stored as a list to builtin variable PRegC. Values used for xList, yList, and frequencyList are stored automatically to builtin variables xStat, yStat, and fStat, respectively. The regression equation is stored also to builtin 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 builtin 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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Chapter 20: A to Z Function and Instruction Reference
Pol † mode screen
4Pol CPLX menu
Pol
Sets polar graphing mode. complexNumber 4Pol Displays complexNumber in polar form (magnitudeangle), 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 (magnitudeangle). magnitudeangle 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)+(3p/4) b (5.16990542093.9226…
PolarGC
Displays graph coordinates in polar form.
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Chapter 20: A to Z Function and Instruction Reference
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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Chapter 20: A to Z Function and Instruction Reference
PwrR STAT CALC menu
Builtin equation variables such as y1, r1, and xt1 are casesensitive. 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 builtin equation variable such as y1, r1, and xt1.
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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 builtin variables xStat, yStat, and fStat, respectively. The regression equation is stored also to builtin 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 builtin 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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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
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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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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 onedigit 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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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 rowechelon 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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Chapter 20: A to Z Function and Instruction Reference
Repeat ‡ program editor CTL menu (Repea shows on menu)
Return
:Repeat condition :commandstorepeat :End :commands
Executes commandstorepeat 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 RungeKutta 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 16bit binary number. When the bits are rotated left, the leftmost bit rotates to the rightmost bit.
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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 AF 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 16bit 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 AF 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 rowechelon 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 builtin 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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123456789
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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 builtin lists xStat, yStat, and fStat in columns 1 through 3, respectively.
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{1 2 3 4} {5 6 7 8} Done
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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 = negativeslope 45¡ 4 = positiveslope 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
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In Bin number base mode:
Returns a real integer with bits shifted one to the left. Internally, integer is represented as a 16bit 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 AF 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 16bit 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 AF
menu. Do not use 1 to type a letter.
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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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[[3 L4] [1 6 ]] [7 6] [3 .5]
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 CayleyHamilton 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 Builtin equation variables such as y1, r1, and xt1 are casesensitive. Do not use Y1, R1, and XT1.
If you specify a period, the TI86 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 builtin equation variable such as y1, r1, and xt1. The equation’s coefficients always are stored as a list to builtin variable PRegC. iterations is optional; it specifies the maximum number of times (1 through 16) the TI86 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.
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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 builtin variables xStat and yStat, respectively. The regression equation is stored also to builtin 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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Done
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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 builtin 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
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{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 builtin variables xStat and yStat for xListName and yListName, respectively. These builtin 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 builtin variables xStat and yStat for xListName and yListName, respectively. These builtin 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 3element 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 builtin 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 builtin 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.
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"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:
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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
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[[(1,L2) (3,L2)] [(1,L1) (4,L3)]]
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TwoVar STAT CALC menu (TwoVa shows on menu)
TwoVar xList,yList,frequencyList
Performs twovariable 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 builtin 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 builtin 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).
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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 :commandswhiletrue :End :command
Executes commandswhiletrue as long as condition is true.
vc4li [2,7,L8,0] b
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{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 J20 : TEMP+1/J¶TEMP : J+1¶J :End :Disp "Reciprocal sums to 20",TEMP ©
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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 builtin variables xStat and yStat. These variables must contain valid data of the same dimension; otherwise, an error occurs.
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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.
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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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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.
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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 builtin variables xFact and yFact; the default is 4 for both factors.
ZIn b
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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 TI86, 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 builtin 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.
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Chapter 20: A to Z Function and Instruction Reference
ZRcl
ZRcl
Sets the window variables to values stored previously in the userdefined zoomwindow variables, and then updates the graph screen.
† GRAPH ZOOM menu
To set userdefined zoomwindow variables, either: • Press 6 ( / / / & (ZSTO) to store the current graph’s window variables. – or – • Store the applicable values to the zoomwindow 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
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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
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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
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379
Appendix
A
Appendix TI86
TI86 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 TI86, 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
TI86 Menu Map This section presents the TI86 menus as they appear on the TI86 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 usercreatedname 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 TI86, 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
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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
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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
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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
CATLGVARS 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
CATLGVARS Selection Menu
4 VECTR MATRX STRNG
EQU
CONS
4
PRGM
 w & or select a data type
PAGE$ PAGE# CUSTM BLANK
99APPX.DOC TI86, 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
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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
Œ
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
'
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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
ltyr
4
’' TIME km2
m0
’ TEMP
CONV LNGTH (Length) Menu LNGTH AREA mm cm
x‡
‘
CONV (Conversions) Menu LNGTH AREA
pEval
USER
CONS BLTIN (BuiltIn Constants) Menu BLTIN Na
%
TEMP acre
4
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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 ftlb kwhr 4
eV
erg
Iatm
99APPX.DOC TI86, 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 ÕÚ Ü
TYPE ß
knot
”(
LIST NAMES Menu OPS
{ fStat
} NAMES EDIT xStat yStat
OPS
”)
The (Number) BASE Menu ÕÚ
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 ÕÚ (Hexadecimal) Menu Õ Ö
TYPE ×
CONV BOOL Ø Ù
—&
BIT Ú
BASE CONV (Conversions) Menu ÕÚ 4Bin
TYPE 4Hex
CONV BOOL 4Oct 4Dec
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Sortx
BIT
—(
390
Appendix —)
BASE BOOL (Boolean) Menu ÕÚ 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 ÕÚ rotR
BIT
EQU
CONS PRGM
4
GDB
PIC
MEM RESET Are You Sure? Menu
ClrEnt
YES
NO
š
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
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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
Ÿ
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 variablename characters, including the first letter. p ( ~) is not valid as a character; p is a constant on the TI86.
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 topright corner, a graph or program has paused; the TI86 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.
99APPX.DOC TI86, Appendix, US English Bob Fedorisko Revised: 02/27/01 1:20 PM Printed: 02/27/01 1:26 PM Page 392 of 26
Appendix
393
Error Conditions When the TI86 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 TI86 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 builtin 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 builtin 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.
99APPX.DOC TI86, Appendix, US English Bob Fedorisko Revised: 02/27/01 1:20 PM Printed: 02/27/01 1:26 PM Page 394 of 26
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 2ndorder or higher differential equation with SlpFld field format set; change field format or modify the order. You attempted to plot a 3rdorder 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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397
Equation Operating System (EOS™) The Equation Operating System (EOS) governs the order of evaluation on the TI86. 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.
Multiargument functions, such as nDeriv(A2,A,6), are evaluated as they are encountered.
TI86 implied multiplication rules differ from those of the TI85. For example, the TI86 evaluates 1à2x as (1à2)¹x, while the TI85 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
Singleargument 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 TI86 recognizes implied multiplication, so you need not press M to express multiplication in all cases. For example, the TI86 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 displayconversion 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 TI86, 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 TI86 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 TI86 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 TI86 carries more digits internally than it displays. Values are stored in memory using up to 14 digits with a 3digit 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 3digit exponent. ♦ Chapter 4 describes calculations in hexadecimal, octal, and binary number bases.
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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: email:
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 email or visit the TI Calculator home page on the World Wide Web. email: [email protected] Internet: education.ti.com
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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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Appendix
Warranty Information Customers in the U.S. and Canada Only OneYear 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 ONEYEAR 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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403
Australia & New Zealand Customers only OneYear 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 oneyear 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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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 ALPHAlock, 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
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assembly language programs, 225 assignment, 270 attached formulas executing, 164 resolving errors, 165 attachedformula 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 ÕÚ (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, 1618 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
builtin constants, 58 builtin 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 QuickFind Locator, 262 CATLG (CATALOG), 43 CATLGVARS (CATALOG Variables) menu, 43 changing TI86 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 (BuiltIn Constants) menu, 58 CONS EDIT menu, 60 consecutive entries, 26 Constant Memory feature, 17, 34 constants, 59 builtin, 58 defined, 58 name, 61 usercreated, 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 freemoving, 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 complexnumber 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 email 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 equationentry 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 freemoving 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
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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 interactivesolver editor, 204 bounds, 204 international letters, 46 Internet downloading programs, 235 email address (TI Customer Support), 392
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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 lowbattery message, 16, 18 lower menu, 32 LU( (lowerupper), 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
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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
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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 orderofevaluation 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 freemoving 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
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drawing, 122 equation editor, 118 freemoving 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 rootfinder, 211 polynomial value, 52 power of 10 (10^), 20, 34, 337 PRegC, 193 previous entries, 8 reexecuting, 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
QuickFind 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 complexnumber 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
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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 complexnumber 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 usercreated 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 (RungeKutta) method, 133, 345 rnorm (row norm), 183, 346 ROOT, 96, 97 x‡, 346 rootfinder, 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
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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
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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 TIGRAPH 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 TI86, 2, 17 turning on TI86, 2, 17 TwoVa (TwoVar), 189, 368
U unevaluated expression storing, 9, 40 units of measure converting, 61 unittounit cable, 234, 235 unitV (unit vector), 173, 368 unknown variable solving for, 206 upper menu, 32
selecting an item, 33 usercreated constants, 43, 58, 60 usercreated 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
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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 (xvariable list), 189
Index xyline, 370
Y y variable, 77 y(x)=, 75 YICPT (yintercept), 96, 100 yScl (scale), 81 yStat (yvariable 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 usercreated zoom variables, 239
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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