TI-86/TI-85 ONLINE Graphing Calculator Manual for Dwyer ...
TI-86/TI-85 ONLINE Graphing Calculator Manual for Dwyer/Gruenwald's
PRECALCULUS
A CONTEMPORARY APPROACH
Dennis Pence
Western Michigan University
Brooks/Cole
Thomson LearningTM Australia ? Canada ? Mexico ? Singapore Spain ? United Kingdom ? United States
COPYRIGHT ? 2004 by Brooks/Cole A division of Thomson Learning The Thomson Learning logo is a trademark used herein under license. For more information, contact: BROOKS/COLE 511 Forest Lodge Road Pacific Grove, CA 93950 USA
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Table of Contents
TI-86/TI-85 Graphing Calculators
Chapter 1
Chapter 2 Chapter 3 Chapter 4 Chapter 5
Foundations and Fundamentals . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 Calculator Fundamentals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 Order of Operation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 Complex Arithmetic . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 Scientific Notation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 Exponents and Radicals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 Fractional Arithmetic . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 Scatter Plots . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 Function Graphing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13 Solving Equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15 Graphing a Circle . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17 Rational Functions and Vertical Asymptotes . . . . . . . . . . . . . 17
Functions and Their Graphs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18 Evaluating Functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18 Increasing and Decreasing, Turning Points . . . . . . . . . . . . . . 20 Combinations and Composition of Functions . . . . . . . . . . . . 20 Inverse Functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20 Graphing a Family of Functions . . . . . . . . . . . . . . . . . . . . . . 21 Piecewise-defined Functions . . . . . . . . . . . . . . . . . . . . . . . . . 21 Least-Squares Best Fit . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22
Polynomial and Rational Functions . . . . . . . . . . . . . . . . . . . . . . . . 24 Polynomial Functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24 Rational Functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26
Exponential and Logarithmic Functions . . . . . . . . . . . . . . . . . . . . 26 Exponential Functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26 Logarithmic Functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27 Regressions Involving Exponentials and Logarithms . . . . . . 27
Trigonometric Functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29 Angle Measurement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29 Sine, Cosine, and Tangent Function Keys . . . . . . . . . . . . . . . 29 Plotting the Sine, Cosine, and Tangent Functions . . . . . . . . . 30 Families of Trigonometric Functions . . . . . . . . . . . . . . . . . . . 31 Cosecant, Secant, and Cotangent Functions . . . . . . . . . . . . . 31 Plotting the Inverses of Sine, Cosine, and Tangent . . . . . . . . 31
Chapter 6 Trigonometric Identities and Equations . . . . . . . . . . . . . . . . . . . . . 32 Graphical Check of Equations . . . . . . . . . . . . . . . . . . . . . . . . 32 Conditional Trigonometric Equations . . . . . . . . . . . . . . . . . . 33
Chapter 7 Applications of Trigonometry . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34 Complex Numbers Revisited . . . . . . . . . . . . . . . . . . . . . . . . . 34 Polar Coordinates . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35 Plotting Polar Equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35 Vectors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37
Chapter 8 Relations and Conic Sections . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38 Graphing Relations in Pieces . . . . . . . . . . . . . . . . . . . . . . . . . 38 Plotting Parabolas . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39 Plotting Hyperbolas . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39 Plotting Parametric Equations . . . . . . . . . . . . . . . . . . . . . . . . 40
Chapter 9 Systems of Equations and Inequalities . . . . . . . . . . . . . . . . . . . . . . 41 Matrices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41 Gaussian Elimination . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41 Identity Matrices, the Inverse of a Matrix, Determinants . . . 42 Systems of Inequalities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44 Linear Programming . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45
Chapter 10 Integer Functions and Probability . . . . . . . . . . . . . . . . . . . . . . . . . . 46 Sequences . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46 Series . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48 Permutations, Combinations, Random Numbers . . . . . . . . . . 48
Note that in Acrobat Reader, each chapter and section in this table of contents is linked to the appropriate location in the document. Similarly, chapter and section titles in the document are linked back to this table of contents. Web links are also active if your computer has an internet connection.
TI-86, TI-85
The TI-86 is a good choice for a graphing calculator to use while learning from Precalculus. The older TI-85 will do most of the activities presented here, but it lacks some editing and statistical features of the newer model. The biggest improvements in the TI-86 are the increased memory and the ability to load and run assembly language programs. You can look at the Texas Instruments graphing calculator web pages () to find some programs that can be downloaded using a computer and the GraphLink cable. Thus the TI-86 should be your choice if you are purchasing a new calculator in this family. However Texas Instruments announced several years ago the intention to stop making this line. The TI-86 seems to be heavily discounted now (probably to sell out the remaining stock). If you are buying a new calculator, I would suggest seriously looking at other TI models with flash ROM which can be upgraded.
Chapter 1 - Foundations and Fundamentals
Calculator Fundamentals When you turn on a TI-86 or TI-85, it usually comes up in the Home screen. If not
(because the calculator did an "automatic shutoff" in another screen), press y k to move to the Home screen where immediate computations are performed. The ` key performs two important activities here. While you are typing a new command line (before ?), pressing ` will clear out everything in the command line. If there is nothing in the command line, pressing ` will clear out all of the previous results still showing in the Home screen.
Press y l so that we can check (and explain) the various mode settings.
TI-85/86 MODE Screen
The first two lines determine how the calculator will display real numbers. Normal (the default) tries to show the entire number normally, but switches to scientific notation if a positive number is too large or too small. Sci always uses scientific notation, and Eng uses a special scientific notation where exponents are a multiple of 3. Float (the default)
TI-86/TI-85, Precalculus
? 2004 Brooks/Cole, a division of Thomson Learning, Inc.
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