Texas Instruments TI-86 User Manual
TI-86
GRAPHING CALCULATOR
GUIDEBOOK
TI-GRAPH LINK, Calculator-Based Laboratory, CBL, CBL 2, Calculator-Based Ranger, CBR, Constant Memory, Automatic Power
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Copyright © 1997, 2001 by Texas Instruments Incorporated
ii
Important
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Instruments shall not be liable for any claim of any kind whatsoever against the use of these materials by any other party.
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This equipment has been tested and found to comply with the limits for a Class B digital device, pursuant to Part 15 of the FCC
rules. These limits are designed to provide reasonable protection against harmful interference in a residential installation. This
equipment generates, uses, and can radiate radio frequency energy and, if not installed and used in accordance with the
instructions, may cause harmful interference with radio communications. However, there is no guarantee that interference will
not occur in a particular installation.
If this equipment does cause harmful interference to radio or television reception, which can be determined by turning the
equipment off and on, you can try to correct the interference by one or more of the following measures:
♦
Reorient or relocate the receiving antenna.
♦
Increase the separation between the equipment and receiver.
♦
Connect the equipment into an outlet on a circuit different from that to which the receiver is connected
♦
Consult the dealer or an experienced radio/television technician for help.
.
Table of Contents
iii
TI-86 Quick Start 1
Preparing to Use Your New TI-86 ..................................................... 2
Installing the AAA Batteries ......................................................... 2
Turning On and Turning Off the TI-86.......................................... 2
Adjusting the Contrast .................................................................2
Resetting All Memory and Defaults.............................................. 3
Calculating on the Home Screen.......................................................3
Calculating the Sine of a Number.................................................3
Storing the Last Answer to a Variable..........................................3
Using a Variable in an Expression ................................................4
Editing an Expression ................................................................... 4
Displaying a Complex Number as a Result...................................5
Using a List with a Function......................................................... 5
Displaying the Integer Part of Real Numbers in a List .................. 6
Removing (Exiting) a Menu..........................................................6
Finding the Square Root............................................................... 7
Calculating Derivatives................................................................. 7
Retrieving, Editing, and Re-evaluating the Previous Entry ...........8
Converting Degrees Fahrenheit to Degrees Celsius...................... 8
Storing an Unevaluated Expression to an Equation Variable .......9
Plotting Functions on the Graph Screen............................................ 9
Displaying and Entering Functions in the Equation Editor............9
Changing the Graph Style of a Function.....................................10
Plotting a Function on the Graph Screen....................................11
Tracing a Function......................................................................11
Evaluating y for a Specific x Value (During a Trace) ................... 12
Changing a Window Variable Value........................................... 12
Deselecting a Function ...............................................................13
Zooming In on a Portion of the Graph Screen ............................ 14
Chapter 1: Operating the TI-86 15
Installing or Replacing Batteries .....................................................16
When to Replace Batteries .........................................................16
Turning On and Turning Off the TI-86.............................................17
Adjusting the Display Contrast........................................................17
The Home Screen ............................................................................18
Displaying Entries and Answers..................................................18
Entering Numbers ...........................................................................19
Entering Negative Numbers .......................................................19
Using Scientific or Engineering Notation....................................20
Entering Complex Numbers........................................................ 20
Entering Other Characters............................................................... 21
The 2nd Key................................................................................21
iv
TI-86 Table of Contents
The ALPHA Key........................................................................... 21
ALPHA-lock and alpha-lock........................................................ 22
Common Cursors........................................................................ 22
Cursor Direction Keys ................................................................. 23
Inserting, Deleting, and Clearing Characters..............................23
Entering Expressions and Instructions ............................................24
Entering an Expression...............................................................24
Using Functions in Expressions ..................................................25
Using an Instruction ................................................................... 25
Entering Functions, Instructions, and Operators ........................25
Entering Consecutive Entries...................................................... 26
The Busy Indicator...................................................................... 26
Interrupting a Calculation or Graph ...........................................26
Diagnosing an Error ........................................................................ 27
Correcting an Error..................................................................... 27
Reusing Previous Entries and the Last Answer ...............................28
Retrieving the Last Entry ............................................................ 28
Retrieving and Editing the Last Entry .........................................28
Retrieving Previous Entries......................................................... 28
Retrieving Multiple Entries......................................................... 29
Clearing the ENTRY Storage Area ..............................................29
Retrieving the Last Answer ........................................................29
Using Ans Preceding a Function.................................................30
Storing Results to a Variable ...................................................... 30
Using TI-86 Menus..........................................................................31
Displaying a Menu......................................................................31
The Menu Keys...........................................................................32
Selecting a Menu Item................................................................32
Exiting (Removing) a Menu ........................................................33
Viewing and Changing Modes ........................................................34
Changing a Mode Setting...........................................................34
Chapter 2: The CATALOG, Variables, and Characters 37
The CATALOG .................................................................................38
Storing Data to Variables ................................................................ 39
Creating a Variable Name ..........................................................39
Storing a Value to a Variable Name ...........................................40
Storing an Unevaluated Expression............................................40
Storing an Answer......................................................................41
Copying a Variable Value ...........................................................41
Displaying a Variable Value........................................................ 41
Recalling a Variable Value..........................................................42
Classifying Variables as Data Types. ...............................................42
The CATLG-VARS (CATALOG-Variables) Menu...........................43
Selecting a Variable Name .........................................................44
The CUSTOM Menu.........................................................................44
Entering CUSTOM Menu Items................................................... 44
Clearing CUSTOM Menu Items...................................................45
Deleting a Variable from Memory ..............................................45
TI-86 Table of Contents
v
The CHAR (Character) Menu...........................................................45
The CHAR MISC (Miscellaneous) Menu...................................... 46
The CHAR GREEK Menu............................................................. 46
The CHAR INTL (International) Menu......................................... 46
Adding a Modifier to a Vowel ....................................................46
Chapter 3: Math, Calculus, and Test Operations 47
Keyboard Mathematical Functions .................................................48
The MATH Menu............................................................................. 49
The MATH NUM (Number) Menu............................................... 49
The MATH PROB (Probability) Menu.......................................... 50
The MATH ANGLE Menu............................................................ 51
The MATH HYP (Hyperbolic) Menu.............................................51
The MATH MISC (Miscellaneous) Menu..................................... 52
The InterpolateàExtrapolate Editor............................................ 53
The CALC (Calculus) Menu.............................................................. 54
The TEST (Relational) Menu............................................................55
Using Tests in Expressions and Instructions ............................... 56
Chapter 4: Constants, Conversions, Bases, and Complex Numbers 57
Using Built-In and User-Created Constants..................................... 58
The CONS (Constants) Menu...................................................... 58
The CONS BLTIN (Built-In Constants) Menu............................... 58
Creating or Redefining a User-Created Constant .......................60
The Constant Editor Menu..........................................................60
Entering a Constant Name in an Expression ..............................61
Converting Units of Measure ..........................................................61
Converting a Unit of Measure ....................................................61
The CONV (Conversions) Menu .................................................. 62
The CONV LNGTH (Length) Menu ..............................................63
The CONV AREA Menu...............................................................63
The CONV VOL (Volume) Menu..................................................63
The CONV TIME Menu................................................................63
The CONV TEMP (Temperature) Menu ....................................... 63
The CONV MASS Menu ..............................................................64
The CONV FORCE Menu.............................................................64
The CONV PRESS (Pressure) Menu ............................................. 64
The CONV ENRGY (Energy) Menu ..............................................64
The CONV POWER Menu............................................................64
The CONV SPEED Menu .............................................................64
Converting a Value Expressed as a Rate ....................................65
Number Bases .................................................................................65
Number Base Ranges .................................................................66
One’s and Two’s Complements .................................................. 66
The (Number) BASE Menu.......................................................... 66
The BASE Õ-Ú (Hexadecimal Characters) Menu.........................67
Entering Hexadecimal Digits.......................................................67
The BASE TYPE Menu.................................................................67
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TI-86 Table of Contents
The BASE CONV (Conversion) Menu .......................................... 68
Converting Number Bases.......................................................... 68
The BASE BOOL (Boolean) Menu ...............................................68
Results of Boolean Operations ................................................... 69
The BASE BIT Menu.................................................................... 69
Using Complex Numbers................................................................. 70
Complex Results......................................................................... 70
Using a Complex Number in an Expression................................ 71
The CPLX (Complex Number) Menu........................................... 71
Chapter 5: Function Graphing 73
Defining a Graph............................................................................. 74
Setting the Graph Mode .................................................................74
The GRAPH Menu ........................................................................... 75
Using the Equation Editor ............................................................... 76
The Equation Editor (GRAPH y(x)=) Menu .................................76
Defining a Function in the Equation Editor ................................77
Notes about Defining Function Equations..................................78
Selecting Graph Styles................................................................ 79
Setting the Graph Style in the Equation Editor........................... 80
Using Shading Patterns to Differentiate Functions..................... 80
Viewing and Changing OnàOff Status of Stat Plots ................... 81
Setting the Window Variables......................................................... 81
Displaying the Window Editor.................................................... 82
Changing a Window Variable Value........................................... 82
Setting Graphing Accuracy with
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
x and @y ...............................83
@
Chapter 6: Graph Tools 87
Graph Tools on the TI-86 ................................................................ 88
The GRAPH Menu.......................................................................88
Using the Free-Moving Cursor....................................................89
Graphing Accuracy .....................................................................89
Tracing a Graph...............................................................................90
Stopping and Resuming a Trace.................................................91
Resizing the Graph Screen with ZOOM Operations.........................91
The GRAPH ZOOM Menu ...........................................................91
Defining a Custom Zoom In........................................................ 93
Setting Zoom Factors..................................................................93
Zooming In and Zooming Out on a Graph..................................93
Storing and Recalling Zoom Window Variable Values................95
Using Interactive Math Functions ...................................................95
The GRAPH MATH Menu............................................................ 95
Settings That Affect GRAPH MATH Operations .......................... 96
Using ROOT, FMIN, FMAX, or INFLC ..........................................97
TI-86 Table of Contents
vii
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
The Table Menus ...................................................................... 112
Setting Up the Table .....................................................................113
Viewing and Editing Dependent Variable Equations ...............114
Clearing the Table.........................................................................114
Chapter 8: Polar Graphing 115
Preview: Polar Graphing ...............................................................116
Defining a Polar Graph..................................................................117
Setting Polar Graphing Mode...................................................117
The GRAPH Menu.....................................................................117
Displaying the Polar Equation Editor........................................118
Setting the Graph Screen Window Variables............................ 118
Setting the Graph Format.........................................................119
Displaying the Graph................................................................119
Using Graph Tools in Pol Graphing Mode.....................................119
The Free-Moving Cursor ........................................................... 119
Tracing a Polar Equation ..........................................................120
Moving the Trace Cursor to a q Value...................................... 121
Using Zoom Operations............................................................ 121
The GRAPH MATH Menu.......................................................... 122
Evaluating an Equation for a Specified q..................................122
Drawing on a Polar Graph........................................................122
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TI-86 Table of Contents
Chapter 9: Parametric Graphing 123
Preview: Parametric Graphing ......................................................124
Defining a Parametric Graph......................................................... 125
Setting Parametric Graphing Mode.......................................... 126
The GRAPH Menu.....................................................................126
Displaying the Parametric Equation Editor............................... 126
Selecting and Deselecting a Parametric Equation ....................127
Deleting a Parametric Equation................................................ 127
Setting the Graph Screen Window Variables............................ 127
Setting the Graph Format......................................................... 128
Displaying the Graph................................................................ 128
Using Graph Tools in Param Graphing Mode................................ 128
The Free-Moving Cursor........................................................... 128
Tracing a Parametric Function.................................................. 128
Moving the Trace Cursor to a t Value.......................................129
Using Zoom Operations............................................................ 129
The GRAPH MATH Menu.......................................................... 130
Evaluating an Equation for a Specified t ..................................130
Drawing on a Parametric Graph............................................... 130
Chapter 10: Differential Equation Graphing 131
Defining a Differential Equation Graph.........................................132
Setting Differential Equation Graphing Mode ..........................132
The GRAPH Menu.....................................................................133
Setting the Graph Format......................................................... 133
Displaying the Differential Equation Editor ..............................134
Setting the Graph Screen Window Variables............................ 135
Setting the Initial Conditions....................................................136
Setting the Axes .......................................................................137
Differential Equation Graphing Tips .........................................137
The Built-In Variable fldPic .......................................................138
Displaying the Graph................................................................138
Entering and Solving Differential Equations..................................139
Graphing in SlpFld Format........................................................ 139
Transforming an Equation into a First-Order System................ 140
Graphing in DirFld Format........................................................141
Graphing a System of Equations in FldOff Format....................142
Solving a Differential Equation for a Specified Value ...............144
Using Graph Tools in DifEq Graphing Mode .................................144
The Free-Moving Cursor ........................................................... 144
Tracing a Differential Equation................................................. 144
Moving the Trace Cursor to a t Value.......................................145
Drawing on a Differential Equation Graph ...............................145
Drawing an Equation and Storing Solutions to Lists.................145
Using ZOOM Operations...........................................................147
Drawing Solutions Interactively with EXPLR.............................148
Evaluating Differential Equations for a Specified t ...................150
TI-86 Table of Contents
ix
Chapter 11: Lists 151
Lists on the TI-86 .......................................................................... 152
The LIST Menu.......................................................................... 152
The LIST NAMES Menu............................................................. 153
Creating, Storing, and Displaying Lists..........................................153
Entering a List Directly in an Expression................................... 153
Creating a List Name by Storing a List .....................................154
Displaying List Elements Stored to a List Name .......................154
Displaying or Using a Single List Element ................................155
Storing a New Value to a List Element..................................... 155
Complex List Elements .............................................................156
The List Editor ............................................................................... 156
The List Editor Menu ................................................................156
Creating a List Name in the Unnamed Column ........................ 157
Inserting a List Name into the List Editor .................................157
Displaying and Editing a List Element ......................................158
Deleting Elements from a List ..................................................158
Removing a List from the List Editor ........................................158
Using List Operations.................................................................... 159
The LIST OPS (Operations) Menu .............................................159
Using Mathematical Functions with Lists .....................................161
Attaching a Formula to a List Name .............................................162
Comparing an Attached List with a Regular List ......................163
Using the List Editor to Attach a Formula ................................163
Using the List Editor With Attached-Formula Lists ................... 164
Executing and Displaying Attached Formulas ..........................164
Handling Errors Related to Attached Formulas.........................165
Detaching a Formula from a List Name....................................166
Editing an Element of a Attached Formula List ........................166
Chapter 12: Vectors 167
Vectors on the TI-86 .....................................................................168
Creating, Storing, and Displaying Vectors.....................................169
The VECTR (Vector) Menu ........................................................169
The VECTR NAMES Menu.........................................................169
Creating a Vector in the Vector Editor......................................169
The Vector Editor Menu............................................................170
Creating a Vector on the Home Screen.....................................170
Creating a Complex Vector.......................................................171
Displaying a Vector...................................................................171
Using a Vector in an Expression ...............................................172
Editing Vector Dimension and Elements...................................172
The VECTR MATH Menu...........................................................173
The VECTR OPS (Operations) Menu..........................................173
The VECTR CPLX (Complex) Menu ...........................................175
Using Mathematical Functions with Vectors.................................176
Chapter 13: Matrices 177
Matrices on the TI-86....................................................................178
Creating, Storing, and Displaying Matrices ...................................178
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TI-86 Table of Contents
The MATRX (Matrix) Menu ......................................................178
The MATRX NAMES Menu ....................................................... 178
Creating a Matrix in the Matrix Editor .....................................178
The Matrix Editor Menu ...........................................................179
Creating a Matrix on the Home Screen ....................................180
Creating a Complex Matrix ......................................................180
Displaying Matrix Elements, Rows, and Submatrices...............181
Using a Matrix in an Expression...............................................181
Editing Matrices in the Matrix Editor .......................................182
Editing Matrices on the Home Screen ......................................182
The MATRX MATH Menu .........................................................183
The MATRX OPS (Operations) Menu........................................ 184
The MATRX CPLX (Complex ) Menu......................................... 185
Using Mathematical Functions with Matrices............................... 185
Chapter 14: Statistics 187
Statistical Analysis on the TI-86.................................................... 188
Setting Up a Statistical Analysis.................................................... 188
The STAT (Statistics) Menu....................................................... 188
Entering Statistical Data........................................................... 189
The LIST NAMES Menu............................................................. 189
The STAT CALC (Calculations) Menu........................................ 189
Automatic Regression Equation Storage.................................. 191
Results of a Statistical Analysis..................................................... 192
The STAT VARS (Statistical Variables) Menu............................ 192
Plotting Statistical Data.................................................................194
The STAT PLOT Status Screen...................................................194
The STAT PLOT Menu ............................................................... 195
Setting Up a Stat Plot ............................................................... 195
Turning On and Turning Off a Stat Plot .................................... 195
The PLOT TYPE Menu (Selecting a Plot Type)...........................196
Plot Type Characteristics ..........................................................196
The STAT DRAW Menu..................................................................199
Forecasting a Statistical Data Value..............................................199
Chapter 15: Equation Solving 201
Preview: The Equation Solver........................................................202
Entering an Equation in the Equation-Entry Editor........................203
Setting Up the Interactive-Solver Editor........................................204
Entering Variable Values ..........................................................204
Controlling the Solution with Bounds and a Guess .................. 204
Editing the Equation.................................................................205
The Solver Menu.......................................................................206
Solving for the Unknown Variable ................................................206
Graphing the Solution...................................................................207
Solver Graph Tools........................................................................207
The Solver ZOOM Menu ...........................................................208
The Simultaneous Equation Solver................................................ 208
Entering Equations to Solve Simultaneously ............................208
Storing Equation Coefficients and Results to Variables............210
The Polynomial Root-Finder..........................................................211
TI-86 Table of Contents
xi
Entering and Solving a Polynomial........................................... 211
Storing a Polynomial Coefficient or Root to a Variable ............ 212
Chapter 16: Programming 213
Writing a Program on the TI-86 ....................................................214
The PRGM Menu ...................................................................... 214
Creating a Program in the Program Editor ...............................214
The Program Editor Menu ........................................................ 215
The PRGM IàO (InputàOutput) Menu...................................... 215
The TI-86 Key Code Diagram ...................................................217
The PRGM CTL Menu ...............................................................218
Entering a Command Line........................................................ 220
Menus and Screens in the Program Editor ...............................220
Running a Program ....................................................................... 221
Breaking (Interrupting) a Program ...........................................222
Working with Programs ................................................................223
Managing Memory and Deleting a Program ............................ 223
Editing a Program.....................................................................223
Calling a Program from Another Program................................224
Copying a Program to Another Program Name........................ 225
Using and Deleting Variables within a Single Program ............225
Running an Assembly Language Program ....................................225
Entering and Storing a String........................................................ 226
The STRNG (String) Menu ........................................................227
Creating a String ......................................................................227
Chapter 17: Memory Management 229
Checking Available Memory .........................................................230
The MEM (Memory) Menu .......................................................230
Checking Memory Usage..........................................................230
Deleting Items from Memory ........................................................231
The MEM DELET (Delete) Menu ...............................................231
Resetting the TI-86 .......................................................................232
The MEM RESET (Reset) Menu.................................................232
ClrEnt (Clear Entry)...................................................................232
Chapter 18: The TI-86 Communication Link 233
TI-86 Linking Options....................................................................234
Linking Two TI-86s...................................................................234
Linking a TI-86 and a TI-85......................................................234
Linking a TI-86 and a CBL 2/CBL or CBR System......................234
Linking a TI-86 and a PC or Macintosh ....................................235
Downloading Programs from the Internet................................235
Connecting the TI-86 to Another Device.......................................235
The LINK Menu......................................................................... 236
Selecting Data to Send..................................................................236
The LINK SEND Menu...............................................................236
Initiating a Memory Backup .....................................................237
Selecting Variables to Send ......................................................238
The SEND WIND (Window Variables) Screen............................238
Sending Variables to a TI-85 ....................................................239
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TI-86 Table of Contents
The LINK SND85 (Send Data to TI-85) Menu ...........................239
Preparing the Receiving Device..................................................... 240
Transmitting Data .........................................................................240
Receiving Transmitted Data.......................................................... 241
Repeating Transmission to Several Devices .............................242
Error Conditions .......................................................................242
Insufficient Memory in Receiving Unit......................................242
Chapter 19: Applications 243
Using Math Operations with Matrices ..........................................244
Finding the Area between Curves................................................. 245
The Fundamental Theorem of Calculus......................................... 246
Electrical Circuits........................................................................... 248
Program: Taylor Series ..................................................................250
Characteristic Polynomial and Eigenvalues................................... 252
Convergence of the Power Series .................................................254
Reservoir Problem......................................................................... 256
Predator-Prey Model..................................................................... 258
Program: Sierpinski Triangle .........................................................260
Chapter 20: A to Z Function and Instruction Reference 261
Quick-Find Locator........................................................................ 262
Alphabetical Listing of Operations................................................ 266
Appendix 379
TI-86 Menu Map...........................................................................380
Handling a Difficulty......................................................................392
Error Conditions ............................................................................393
Equation Operating System (EOSé)..............................................397
Implied Multiplication ..............................................................397
Parentheses..............................................................................397
TOL (The Tolerance Editor)............................................................398
Computational Accuracy ............................................................... 399
Support and Service Information...................................................400
Product Support........................................................................400
Product Service.........................................................................401
Other TI Products and Services.................................................401
Warranty Information....................................................................402
Customers in the U.S. and Canada Only...................................402
Australia & New Zealand Customers Only................................403
All Customers outside the U.S. and Canada.............................404
Index
TI-86 Quick Start
Preparing to Use Your New TI-86........................................ 2
Calculating on the Home Screen.......................................... 3
Plotting Functions on the Graph Screen .............................. 9
M1 M2
F1 F2 F3
-
TI 86
M3
M4
M5
F4
F5
2
Quick Start
After about four minutes of
inactivity, the TI-86 turns off
automatically.
$
If you release
or # while
adjusting the contrast, you
-
must press
again to
continue the adjustment.
Preparing to Use Your New TI-86
The brief examples in the TI-86 Quick Start demonstrate some common TI-86 features.
Before you begin, you must install the batteries, turn on the calculator, adjust the contrast,
and reset the memory and the defaults. Chapter 1 has more details on these topics.
Installing the AAA Batteries
Four AAA batteries are included in the TI-86 retail package. Remove the batteries from the
package and install them in the battery compartment on the back of the calculator. Arrange
N
the batteries according to the polarity (+ and
Turning On and Turning Off the TI-86
To turn on the TI-86, press ^, which is in the bottom-left corner of the
keyboard. You should see the entry cursor ( Å ) blinking in the top-left
corner of the screen. If you do not see it, adjust the contrast (see below).
To turn off the calculator, press -, and then the key under
^
. This guidebook uses brackets ( ã and ä ) to express - and
keystroke combinations. For example, to turn off the TI-86, press - .
Adjusting the Contrast
Press and release the yellow - key.
Press and hold $ or # (above or below the half-shaded circle).
♦
To darken the screen contrast, press and hold $.
♦
To lighten the screen contrast, press and hold #.
) diagram in the battery compartment.
, which is
OFF
1
MODE
QUIT
EXIT
LINK
x-VAR
MORE
x
INS
DEL
alpha
ALPHA
2nd
=
RCL
BASE
ST
O
1
CHAR
OFF
ON
0
U
Y
To express - and
keystroke combinations, this
guidebook places brackets
ä
ã
and
around the word
)
(
above the key to press.
The TI-86 on-screen division
symbol is a forward slash
, as in a fraction.
( à )
Following evaluation, the
entry cursor automatically
moves to the next line, ready
for a new entry.
When the TI-86 evaluates an
expression, it automatically
stores the answer to the builtin variable
any previous value.
Ans
1
, replacing
Quick Start
Resetting All Memory and Defaults
To reset all memory and defaults, press -
Defaults set
are displayed on the home screen, confirming that all memory and defaults are
™ ( & )
. The messages
Mem cleared
and
reset. You may need to adjust the contrast after memory and default reset.
Calculating on the Home Screen
To replicate the screens shown in the Quick Start activities, reset all memory and defaults
once before you begin. Before doing an activity, press
before the entry retrieval and integer-part examples). Otherwise, the screens your TI-86
shows may differ from the screens pictured next to the activities.
Calculating the Sine of a Number
Enter the sine function. (
Enter a value. You can enter an expression,
which is evaluated when you press
Evaluate the problem. The evaluation of the
b
expression sine(pà4) is displayed.
:) =
D - ~ F
.
b
Storing the Last Answer to a Variable
Paste the store symbol (
Since a value must precede
not enter a value, the TI-86 automatically
Ans
pasted
before ¶. (
¶
) to the screen.
¶
, but you did
continued
:
(
X
)
:
)
to clear the screen (except
4
E
3
4
Quick Start
When ALPHA-lock is on and
you press a key, the letters
printed in blue above the
keys are pasted to the
screen. In the ex a m p l e , p r e s s
Z
to enter a V.
You need not move the
cursor to the end of the line
to evaluate the expression.
Enter the variable name to which you want
to store the last answer. ALPHA-lock is on.
Store the last answer to the variable. The
stored value is displayed on the next line.
Using a Variable in an Expression
Enter the variable, and then square it. (:)
Evaluate. The value stored to the variable
V
is squared and displayed.
Editing an Expression
Enter the expression
Change
Move the cursor to the beginning of the
3.2
to
expression and insert a value. The insert
cursor blinks between
Evaluate. The result is displayed. b
(25+14)(4N3.2)
2.3
. ! ! ! ! 2 "
3
and 25.
.(:)
ä
ã
V
b
ä
ã
1
I
V
b
25
D
\ 14 E
4
D
T 3 ` 2 E
- ! - p
3
3
a
negates a value, as in
T
subtracts, as in
An ellipsis (...) indicates that
the result continues beyond
the screen.
5N2=3
2
L
.
Displaying a Complex Number as a Result
.
Enter the natural log function. (:) B
Enter a negative number. D a
Evaluate. The result is displayed as a
complex number.
Using a List with a Function
Enter the exponential function. (:) - ‚
Display the
open brace (
On the TI-86,
list.
menu, and then select the
LIST
{
) from the
{
specifies the beginning of a
LIST
menu.
2
E
b (press "
to display more)
- ”
&
LIST
menu
Quick Start
5
Enter the list elements. Separate each
element from the next with a comma.
Select the close brace (
}
) from the
menu to specify the end of the list.
Evaluate. The results of the constant
raised to the 5th, 10th, and 15th powers are
displayed as list elements.
LIST
e
5
P 10 P
15
'
b (press "
to display more)
6
Quick Start
Displaying the Integer Part of Real Numbers in a List
Display the
automatically replaces the
the last activity.)
Select
NUM
menu. The
Select the
the
MATH NUM
menu. (The
MATH
to display the
menu shifts up.
MATH
iPart
(integer part) function from
iPart
menu.
MATH
menu from
LIST
MATH NUM
is pasted to the
menu
- Œ
MATH
&
MATH NUM
'
menu
menu
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
Display the integer part of the result list
Ans
.)
b
elements from the previous activity.
Removing (Exiting) a Menu
In the previous example, the
MATH NUM
Remove the
menu are displayed (- Π&).
MATH NUM
menu from the screen. .
MATH
menu and the
Remove the
menu from the screen. .
MATH
Finding the Square Root
Paste the square root function to the screen. (:) - ˆ
Quick Start
7
Enter a value for which you want to find the
square root.
Evaluate the expression. The square root of
144
is displayed.
Calculating Derivatives
Display the
der1
.
Enter an expression (
variable (
Evaluate. The first derivative of
x
respect to
menu, and then select
CALC
2
x
) with respect to a
) at a given point (8).
x
at 8 is displayed.
x
2
with
144
b
(:)
- †
(
CALC
menu
2 I P 2
P 8 E
b
8
When you press
TI-86 stores the expression
or instruction you entered to
the built-in memory storage
area called
When expressing a
measurement for a
conversion, you do not enter
a unit symbol manually. For
example, you need not enter
¡
Quick Start
b
.
ENTRY
to designate degrees.
, the
Retrieving, Editing, and Re-evaluating the Previous Entry
Retrieve the last entry from the previous
- ¢
example. (The last activity was not cleared.)
Edit the retrieved entry. ! !
2
Evaluate. The first derivative of
respect to
x
at 3 is displayed.
x
with
3
b
Converting Degrees Fahrenheit to Degrees Celsius
Display the
Display the
menu shifts up and
Enter the known measurement. If the
measurement is negative, use parentheses.
In this example, if you omit parentheses,
the TI-86 converts 4¡F to about
which it then negates (changes the sign
of), returning a positive 15.5¡C.
¡
Select
F
to designate Fahrenheit as the
known measurement unit.
conversion symbol ( 4 ) are displayed after
the measurement. (
menu. (:) - ’
CONV
CONV TEMP
TEMP
menu. The
CONV
is highlighted.
*
D a
L
15.5¡C,
'
¡
F
and the
continued
)
4
E
When storing to an equation
variable using
equation variable first, then
and then the unevaluated
expression. This is the
opposite from the order for
storing to most other
variables on the TI-86.
=
, enter the
Quick Start
¡
C
Select
to which you want to convert.
Convert. The ¡C equivalent of
displayed.
to designate Celsius as the unit
L
4¡F is
&
b
Storing an Unevaluated Expression to an Equation Variable
Enter the built-in equation variable
=
,
Enter the equals sign (=). 1
Enter an expression in terms of
Store the expression.
y1
.(:) - n
x
.
The next section shows how to graph the functions
ä
ã
=
5
D = 2 E
b
y1=5(sin x)
ã
Y
ä
1
and
y2=5(cos x)
.
Plotting Functions on the Graph Screen
The TI-86 plots four types of functions on the graph screen. To plot a graph, you must store
an unevaluated expression to a built-in equation variable.
Each activity in this section builds upon the activity that precedes it. You must start here
and perform the activities in the sequence in which they are presented. The first activity in
this section assumes you are continuing from the last activity in the previous section.
Displaying and Entering Functions in the Equation Editor
Display the
GRAPH
menu. (
continued
) 6
9
10
Quick Start
In the equation editor, you
must express each equation
in terms of the independent
variable
mode only; Chapter 5).
To display up to seven graph
styles, depending on the
graphing mode, repeat
x
(in
Func
graphing
(
.
y(x)=
Select
display the equation editor.
unevaluated expression stored to
from the
GRAPH
menu to
5(sin x)
is the
y1
previous activity. The equation editor
menu is displayed as the lower menu.
Move the cursor down. The
y2=
prompt is
in the
&
equation
editor menu
#
displayed.
Enter the expression
5(cos x)
at the
y2=
5
D > 2 E
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).
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.
Move the cursor to
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
menu to set ¼ (thick) graph style for
y1
. $
from the equation editor
y1
/
(
.
graph style icons
Plotting a Function on the Graph Screen
GRAPH
Select
from the
GRAPH
menu to
plot the graph on the graph screen. The xand y-axes and
GRAPH
menu are
displayed. Then each selected graph is
plotted in the order in which it is listed in
the equation editor.
When the graph is plotted, you can move
the free-moving cursor (
+
) around the
graph screen. The cursor coordinates are
displayed at the bottom of the graph.
Tracing a Function
TRACE
Select
from the
GRAPH
menu to
activate the trace cursor, with which you
can trace along the graph of any selected
function. The number of the current
function (the
1
in y1) is displayed in the
top-right corner.
Move the trace cursor from the function
to the function y2. The 1 in the top-right
corner changes to
the value of
2
; the y value changes to
y2
x=0
at
. (
continued
y1
)
- i
" # ! $
)
$
Quick Start
free-moving cursor
trace cursor
11
12
Quick Start
The window variables values
determine the dimensions of
the graph screen.
Trace the function
displayed
5(cos x)
y
value is the solution for
at the current x value, which also
y2
. As you trace, the
" and !
is displayed on the screen.
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,
x=
the
prompt is displayed.
y2
Evaluate
x=6
at
. The trace cursor
moves directly to the solution. The
or solution of the equation at
x
, is
displayed on the screen.
y
value,
6
b
Changing a Window Variable Value
Display the
Select
GRAPH
WIND
display the window editor.
(
menu. 6
from the
GRAPH
menu to
continued
'
)
Quick Start
13
Change the value stored in the
window variable to 0.
Plot the graph on the redefined graph
screen. Since
fourth quadrants of the graph plane are
displayed.
xMin=0
, only the first and
xMin
Deselecting a Function
y(x)=
Select
display the equation editor and equation
editor menu. The
y(x)=
and
Select
menu to deselect the function
equals sign is no longer highlighted.
Plot the graph on the graph screen. Since
you deselected
To select a function in the equation editor,
repeat these steps. (
and deselects functions.)
from the
is highlighted.
SELCT
from the equation editor
GRAPH
GRAPH
y1
, the TI-86 only plots y2.
SELCT
menu to
menu shifts up
y1=
both selects
0
*
&
*
. The
- i
14
Quick Start
Zooming In on a Portion of the Graph Screen
ZOOM
Select
menu. The
ZOOM
is highlighted.
to display the
GRAPH
menu shifts up and
GRAPH ZOOM
(
BOX
Select
to activate the zoom-box cursor.
Move the zoom-box cursor to a point that is
to be a corner of the redefined graph screen,
and then mark the point with a small square.
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.
Clear the menus from the graph screen.
from the
GRAPH ZOOM
menu
&
" # ! $
b
" # ! $
b
:
Operating
1
Installing or Replacing Batteries ........................................ 16
Turning On and Turning Off the TI-86 ...............................17
Adjusting the Display Contrast ..........................................17
The Home Screen............................................................... 18
Entering Numbers.............................................................. 19
Entering Other Characters .................................................20
Entering Expressions and Instructions ...............................24
Diagnosing an Error ........................................................... 27
Reusing Previous Entries and the Last Answer ..................28
Using TI-86 Menus ............................................................31
Viewing and Changing Modes........................................... 34
the TI-86
M1 M2
F1 F2 F3
-
TI 86
M3
M4
M5
F4
F5
16
To express - and
keystroke combinations, this
guidebook places brackets
( ã and ä )
above the key to press.
Do not remove the lithium
backup battery unless four
fresh AAA batteries are in
place.
Properly dispose of the old
batteries.
If you do not use your TI-86
frequently, the AAA batteries
could last more than two
weeks after the first lowbattery message.
Chapter 1: Operating the TI-86
1
around the word
Installing or Replacing Batteries
Your new TI-86 includes four AAA alkaline batteries. You must install them before you can
turn on the calculator. A lithium backup battery is installed in the calculator already.
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.
Remove all four old batteries.
Install four new AAA alkaline batteries, arranged according to the polarity (+ and N) diagram
inside the battery compartment.
Replace the battery cover by inserting the two prongs into the two slots at the bottom of the
battery compartment, and then push the cover until the latch snaps closed.
When to Replace Batteries
When the AAA batteries are low, a low-battery message is
displayed as you turn on the calculator. Generally, the
calculator will continue to operate for one or two weeks
after the low-battery message is first displayed.
Eventually, the TI-86 will turn off automatically and will
not operate until you replace the AAA batteries.
The lithium backup battery is inside the battery compartment, above the AAA batteries. It
retains all memory when the AAA batteries are low or have been removed. To avoid loss of
data, do not remove the lithium battery unless four fresh AAA batteries are installed.
Replace the lithium backup battery about every three or four years.
Chapter 1: Operating the TI-86
17
Properly dispose of the old
battery.
$
If you release
or # while
adjusting the contrast, you
-
must press
again to
continue the adjustment.
To replace the lithium backup battery, remove the battery cover and unscrew the tiny
screw holding the
BACK UP BATTERY
according to the polarity (+ and
cover in place. Install a new
N
) diagram on the cover. Replace the cover and screw.
CR1616
or
CR1620
battery
Turning On and Turning Off the TI-86
To turn on the TI-86, press ^.
♦
previously had turned off the calculator by
If you
pressing - , the TI-86 clears any errors and
displays the home screen as it was last displayed.
♦
If Automatic Power Down
TM
(APDTM) previously had
turned off the calculator, the TI-86 will return as you
left it, including the display, cursor, and any error.
To turn off the TI-86 manually, press - . All settings and memory contents are
TM
retained by the Constant Memory
feature. Any error condition is cleared.
APD turns off the TI-86 automatically after about four minutes of non-use to extend battery life.
RCL
ST
OFF
PRQ
,
=
O
ON
CONV
CONS
4
BASE TES MEM
T
U
VW
1
2
:
CHAR
Y
Z
0
STRNG
ANS
S
65
3
(
(
Adjusting the Display Contrast
Press and release the yellow - key.
MODE
Press and hold $ or # (above or below the half-shaded circle).
♦
To darken the screen contrast, press and hold $.
♦
To lighten the screen contrast, press and hold #.
2nd
alpha
ALPHA
QUIT
LINK
EXIT
x-VAR
MORE
x
INS
DEL
18
Chapter 1: Operating the TI-86
The TI-86 has 40 contrast
settings, so each number
0
through 9 represents four
settings.
You need not clear the home
screen to begin a new entry.
You can adjust the display contrast anytime to suit your viewing angle and lighting
0
conditions. As you adjust, a number from
(lightest) to 9 (darkest) in the top-right corner
indicates the current contrast setting. The number is not visible when the contrast is
extremely light or dark.
As the batteries weaken over time, the actual contrast level of each number shifts. For
3
example, say you set the contrast to
4
need to set the contrast to
, then 5, then 6, and so on, to retain the original contrast level.
with fresh batteries. As the batteries weaken, you will
However, you need not replace the batteries until the low-battery message is displayed.
The Home Screen
When you first turn on your TI-86, the home screen is displayed. Initially, the home screen
is a blank screen, except for the entry cursor ( Å ) in the top-left corner. If you do not see
the cursor, press -, and then press and hold # or $ to adjust the contrast (page 17).
On the home screen, you can enter and evaluate expressions, and view the results. You also
can execute instructions, store and recall variable values, and set up graphs and editors.
To return to the home screen from any other screen, press -
Displaying Entries and Answers
The home screen displays up to eight lines with a maximum of 21 characters per line. If an
expression or series of instructions exceeds 21 characters and spaces, it automatically
continues on the next line.
After all eight lines are full, text scrolls off the top of the display. You can press $ to scroll
up the home screen, only as far as the first character in the current entry. To retrieve, edit,
and re-execute previous entries, use -
¢
(page 28).
l
.
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