by Earl Swokowski and Jeffery A. Cole
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Taking a unit-circle first approach, this proven book helps students learn, understand, and appreciate trigonometry without compromising mathematical integrity. The book incorporates the use of the graphing calculator (although use of the graphing calculator is not required). Numerous application problems are used throughout to help motivate students toward success in learning trigonometry.
1. TOPICS FROM ALGEBRA.
Real Numbers.
Rectangular Coordinate Systems and Graphs.
Functions. Graphs of Functions.
Inverse Functions.
Exponential and Logarithmic Functions.
Chapter 1 Review Exercises.
Chapter 1 Discussion Exercises.
2. THE TRIGONOMETRIC FUNCTIONS.
Angles.
The Trigonometric Functions.
Graphs of the Trigonometric Functions.
Trigonometric Functions of Angles.
Values of the Trigonometric Functions.
Trigonometric Graphs.
Additional Trigonometric Graphs.
Applied Problems.
Chapter 2 Review Exercises.
Chapter 2 Discussion Exercises.
3. ANALYTIC TRIGONOMETRY.
Verifying Trigonometric Identities.
Trigonometric Equations.
The Addition and Subtraction Formulas.
Multiple-Angle Formulas.
Product-to-Sum and Sum-to-Product Formulas.
The Inverse Trigonometric Functions.
Chapter 3 Review Exercises.
Chapter 3 Discussion Exercises.
4. APPLICATIONS OF TRIGONOMETRY.
The Law of Sines.
The Law of Cosines.
Trigonometric Form for Complex Numbers.
De Moivre's Theorem and nth Roots of Complex Numbers.
Vectors.
The Dot Product.
Chapter 4 Review Exercises.
Chapter 4 Discussion Exercises.
5. EXPONENTIAL AND LOGARITHMIC FUNCTIONS.
Exponential Functions.
The Natural Exponential Function.
Logarithmic Functions.
Properties of Logarithms.
Exponential and Logarithmic Equations.
Chapter 5 Review Exercises.
Chapter 5 Discussion Exercises.
6. TOPICS FROM ANALYTIC GEOMETRY.
Parabolas.
Ellipses.
Hyperbolas.
Plane Curves and Parametric Equations.
Polar Coordinates.
Polar Equations of Conics.
Chapter 6 Review Exercises.
Chapter 6 Discussion Exercises.
APPENDIXES.
I: Using a TI-82/83 Graphing Calculator.
II: Common Graphs and Their Equations.
III: A Summary of Graphs Transformations.
IV: Graphs of Trigonometric Functions and Their Inverses.
V: Complex Numbers.
VI: Lines
ANSWERS TO SELECTED EXERCISES.
INDEX OF APPLICATIONS.
INDEX.
Earl Swokowski and Jeffery A. Cole
ISBN13: 978-0534361280Taking a unit-circle first approach, this proven book helps students learn, understand, and appreciate trigonometry without compromising mathematical integrity. The book incorporates the use of the graphing calculator (although use of the graphing calculator is not required). Numerous application problems are used throughout to help motivate students toward success in learning trigonometry.
Table of Contents
1. TOPICS FROM ALGEBRA.
Real Numbers.
Rectangular Coordinate Systems and Graphs.
Functions. Graphs of Functions.
Inverse Functions.
Exponential and Logarithmic Functions.
Chapter 1 Review Exercises.
Chapter 1 Discussion Exercises.
2. THE TRIGONOMETRIC FUNCTIONS.
Angles.
The Trigonometric Functions.
Graphs of the Trigonometric Functions.
Trigonometric Functions of Angles.
Values of the Trigonometric Functions.
Trigonometric Graphs.
Additional Trigonometric Graphs.
Applied Problems.
Chapter 2 Review Exercises.
Chapter 2 Discussion Exercises.
3. ANALYTIC TRIGONOMETRY.
Verifying Trigonometric Identities.
Trigonometric Equations.
The Addition and Subtraction Formulas.
Multiple-Angle Formulas.
Product-to-Sum and Sum-to-Product Formulas.
The Inverse Trigonometric Functions.
Chapter 3 Review Exercises.
Chapter 3 Discussion Exercises.
4. APPLICATIONS OF TRIGONOMETRY.
The Law of Sines.
The Law of Cosines.
Trigonometric Form for Complex Numbers.
De Moivre's Theorem and nth Roots of Complex Numbers.
Vectors.
The Dot Product.
Chapter 4 Review Exercises.
Chapter 4 Discussion Exercises.
5. EXPONENTIAL AND LOGARITHMIC FUNCTIONS.
Exponential Functions.
The Natural Exponential Function.
Logarithmic Functions.
Properties of Logarithms.
Exponential and Logarithmic Equations.
Chapter 5 Review Exercises.
Chapter 5 Discussion Exercises.
6. TOPICS FROM ANALYTIC GEOMETRY.
Parabolas.
Ellipses.
Hyperbolas.
Plane Curves and Parametric Equations.
Polar Coordinates.
Polar Equations of Conics.
Chapter 6 Review Exercises.
Chapter 6 Discussion Exercises.
APPENDIXES.
I: Using a TI-82/83 Graphing Calculator.
II: Common Graphs and Their Equations.
III: A Summary of Graphs Transformations.
IV: Graphs of Trigonometric Functions and Their Inverses.
V: Complex Numbers.
VI: Lines
ANSWERS TO SELECTED EXERCISES.
INDEX OF APPLICATIONS.
INDEX.