Table of Contents

1. Trigonometric Functions

1.1 Angles
1.2 Angle Relationships and Similar Triangles
1.3 Trigonometric Functions
1.4 Using the Definitions of the Trigonometric Functions

2. Acute Angles and Right Triangles

2.1 Trigonometric Functions of Acute Angles
2.2 Trigonometric Functions of Non-Acute Angles
2.3 Finding Trigonometric Function Values Using a Calculator
2.4 Solving Right Triangles
2.5 Further Applications of Right Triangles

3. Radian Measure and the Unit Circle

3.1 Radian Measure
3.2 Applications of Radian Measure
3.3 The Unit Circle and Circular Functions
3.4 Linear and Angular Speed

4. Graphs of the Circular Functions

4.1 Graphs of the Sine and Cosine Functions
4.2 Translations of the Graphs of the Sine and Cosine Functions
4.3 Graphs of the Tangent and Cotangent Functions
4.4 Graphs of the Secant and Cosecant Functions
4.5 Harmonic Motion

5. Trigonometric Identities

5.1 Fundamental Identities
5.2 Verifying Trigonometric Identities
5.3 Sum and Difference Identities for Cosine
5.4 Sum and Difference Identities for Sine and Tangent
5.5 Double-Angle Identities
5.6 Half-Angle Identities

6. Inverse Circular Functions and Trigonometric Equations

6.1 Inverse Circular Functions
6.2 Trigonometric Equations I
6.3 Trigonometric Equations II
6.4 Equations Involving Inverse Trigonometric Functions
 
7. Applications of Trigonometry and Vectors

7.1 Oblique Triangles and the Law of Sines
7.2 The Ambiguous Case of the Law of Sines
7.3 The Law of Cosines
7.4 Vectors, Operation, and the Dot Product
7.5 Applications of Vectors

8. Complex Numbers, Polar Equations, and Parametric Equations

8.1 Complex Numbers
8.2 Trigonometric (Polar) Form of Complex Numbers
8.3 The Product and Quotient Theorems
8.4 De Moivre's Theorem; Powers and Roots of Complex Numbers
8.5 Polar Equations and Graphs
8.6 Parametic Equations, Graphs, and Applications

Appendix A. Equations and Inequalities

Appendix B. Graphs of Equations

Appendix C. Functions

Appendix D. Graphing Techniques