Trigonometry

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

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