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## Summary

## Author Biography

**Mark Dugopolski**was born in Menominee, Michigan. After receiving a BS from Michigan State University, he taught high school in Illinois for four years. He received an M.S. in mathematics from Northern Illinois University at DeKalb. He then received a PhD in the area of topology and an MS in statistics from the University of Illinois at Champaign–Urbana. Mark taught mathematics at Southeastern Louisiana University in Hammond for twenty-five years and now holds the rank of Professor Emeritus of Mathematics. He has been writing textbooks since 1988. He is married and has two daughters. In his spare time he enjoys tennis, jogging, bicycling, fishing, kayaking, gardening, bridge, and motorcycling.

## Table of Contents

**P. Algebraic Prerequisites**

P.1 The Cartesian Coordinate System

P.2 Functions

P.3 Families of Functions, Transformations, and Symmetry

P.4 Compositions and Inverses

Chapter P Highlights

Chapter P Review Exercises

Chapter P Test

**1. Angles and the Trigonometric Functions**

1.1 Angles and Degree Measure

1.2 Radian Measure, Arc Length, and Area

1.3 Angular and Linear Velocity

1.4 The Trigonometric Functions

1.5 Right Triangle Trigonometry

1.6 The Fundamental Identity and Reference Angles

Chapter 1 Highlights

Chapter 1 Review Exercises

Chapter 1 Test

**2. Graphs of the Trigonometric Functions**

2.1 The Unit Circle and Graphing

2.2 The General Sine Wave

2.3 Graphs of the Secant and Cosecant Functions

2.4 Graphs of the Tangent and Cotangent Functions

2.5 Combining Functions

Chapter 2 Highlights

Chapter 2 Review Exercises

Chapter 2 Test

Tying it all Together

**3. Trigonometric Identities**

3.1 Basic Identities

3.2 Verifying Identities

3.3 Sum and Difference Identities for Cosine

3.4 Sum and Difference Identities for Sine and Tangent

3.5 Double-Angle and Half-Angle Identities

3.6 Product and Sum Identities

Chapter 3 Highlights

Chapter 3 Review Exercises

Chapter 3 Test

Tying it all Together

**4. Solving Conditional Trigonometric Equations**

4.1 The Inverse Trigonometric Functions

4.2 Basic Sine, Cosine, and Tangent Equations

4.3 Multiple-Angle Equations

4.4 Trigonometric Equations of Quadratic Type

Chapter 4 Highlights

Chapter 4 Review Exercises

Chapter 4 Test

Tying it all Together

**5. Applications of Trigonometry**

5.1 The Law of Sines

5.2 The Law of Cosines

5.3 Area of a Triangle

5.4 Vectors

5.5 Applications of Vectors

Chapter 5 Highlights

Chapter 5 Review Exercises

Chapter 5 Test

Tying it all Together

**6. Complex Numbers, Polar Coordinates, and Parametric Equations**

6.1 Complex Numbers

6.2 Trigonometric Form of Complex Numbers

6.3 Powers and Roots of Complex Numbers

6.4 Polar Equations

6.5 Parametric Equations

Chapter 6 Highlights

Chapter 6 Review Exercises

Chapter 6 Test

Tying it all Together

Appendix A: Solutions to Try This Exercise

Appendix B: More Thinking Outside the Box

Answers to All Exercises