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# Trigonometry

**by**Ratti, J. S.; McWaters, Marcus S.

### 9780321567987

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## Summary

## Author Biography

**J.S.Ratti **has been teaching mathematics at all levels for over 35 years. He is currently a full professor of mathematics and director of the "Center for Mathematical Services" at the University of South Florida. Professor Ratti is the author of numerous research papers in analysis, graph theory, and probability. He has won several awards for excellence in undergraduate teaching at University of South Florida and known as the coauthor of a successful finite mathematics textbook.

**Marcus McWaters**is currently the chair of the Mathematics Department at the University of South Florida, a position he has held for the last eight years. Since receiving his PhD in mathematics from the University of Florida, he has taught all levels of undergraduate and graduate courses, with class sizes ranging from 3 to 250. As chair, he has worked intensively to structure a course delivery system for lower level courses that would improve the low retention rate these courses experience across the country. When not involved with mathematics or administrative activity, he enjoys playing racquetball, spending time with his two daughters, and traveling the world with his wife.

## Table of Contents

1. Trigonometric Functions

1.1. Angles

1.2. Triangles

1.3. Trigonometric Functions

1.4. Reference Angles

1.5. Fundamental Trigonometric Identities

Summary

Review

Practice Test

2. Right Triangle Trigonometry

2.1. Trigonometric Functions of an Acute Angle

2.2. Solving Right Triangles

2.3. Additional Applications of Right Triangles

Summary

Review

Practice Test

3. Radian Measure and Circular Functions

3.1. Radian Measure

3.2. Applications of Radian Measure

3.3. The Unit Circle and Circular Functions

3.4. Angular and Linear Speed

Summary

Review

Practice Test

4. Graphs of the Circular Functions

4.1. Graphs of the Circular Functions

4.2. Amplitude and Period

4.3. Translations of the Graphs of Circular Functions

Summary

Review

Practice Test

5. Trigonometric Identities

5.1. Verifying Identities

5.2. Sum and Difference Identities

5.3. Double-Angle and Half-Angle Identities

5.4. Product-to-Sum and Sum-to-Product Identities

Summary

Review

Practice Test

6. Inverse Functions and Trigonometric Equations

6.1. Inverse Trigonometric Functions

6.2. Trigonometric Equations I

6.3. Trigonometric Equations II

Summary

Review

Practice Test

7. Applications of Trigonometric Functions

7.1. The Law of Sines

7.2. The Law of Sines: Ambiguous Case

7.3. The Law of Cosines

7.4. Area of a Triangle

Summary

Review

Practice Test

8. Vectors

8.1. Geometric Vectors

8.2. Algebraic Vectors

8.3. The Dot Product

Summary

Review

Practice Test