**1 RIGHT TRIANGLE RATIOS 1**

**1.1** Angles, Degrees, and Arcs **2**

**1.2** Similar Triangles **13**

**1.3** Trigonometric Ratios and Right Triangles
**22**

**1.4** Right Triangle Applications **33**

*Chapter 1 Group Activity: A Logistics Problem*
**44**

*Chapter 1 Review* **45**

**2 TRIGONOMETRIC FUNCTIONS 51**

**2.1** Degrees and Radians **52**

**2.2** Linear and Angular Velocity **65**

**2.3** Trigonometric Functions: Unit Circle Approach
**72**

**2.4** Additional Applications **84**

**2.5** Exact Values and Properties of Trigonometric
Functions **98**

*Chapter 2 Group Activity: Speed of Light in Water*
**112**

*Chapter 2 Review* **114**

**3 GRAPHING TRIGONOMETRIC FUNCTIONS 121**

**3.1** Basic Graphs **123**

**3.2** Graphing and **138**

**3.3** Graphing and **157**

**3.4** Additional Applications **172**

**3.5** Graphing the Sum of Functions **187**

**3.6** Tangent, Cotangent, Secant, and Cosecant Functions
Revisited **199**

*Chapter 3 Group Activity: Predator–Prey Analysis
Involving Coyotes and Rabbits* **211**

*Chapter 3 Review* **212**

*Cumulative Review Exercise, Chapters 1–3*
220

**4 IDENTITIES 227**

**4.1** Fundamental Identities and Their Use **228**

**4.2** Verifying Trigonometric Identities **235**

**4.3** Sum, Difference, and Cofunction Identities
**245**

**4.4** Double-Angle and Half-Angle Identities **256**

**4.5** Product–Sum and Sum–Product Identities
**267**

*Chapter 4 Group Activity: From to* **275**

*Chapter 4 Review* **277**

**5 INVERSE TRIGONOMETRIC FUNCTIONS; TRIGONOMETRIC EQUATIONS
AND INEQUALITIES 285**

**5.1** Inverse Sine, Cosine, and Tangent Functions
**286**

**5.2** Inverse Cotangent, Secant, and Cosecant Functions
**307**

**5.3** Trigonometric Equations: An Algebraic Approach
**314**

**5.4** Trigonometric Equations and Inequalities: A Graphing
Calculator Approach **327**

*Chapter 5 Group Activity: and* **336**

*Chapter 5 Review* **337**

*Cumulative Review Exercise, Chapters 1–5*
343

**6 ADDITIONAL TOPICS: TRIANGLES AND VECTORS 349**

**6.1** Law of Sines **350**

**6.2** Law of Cosines **365**

**6.3** Areas of Triangles **376**

**6.4** Vectors **383**

**6.5** The Dot Product **399**

*Chapter 6 Group Activity: The SSA Case and the Law of
Cosines* **409**

*Chapter 6 Review* **410**

**7 POLAR COORDINATES; COMPLEX NUMBERS 421**

**7.1** Polar and Rectangular Coordinates **422**

**7.2** Sketching Polar Equations **431**

**7.3** The Complex Plane **444**

**7.4** De Moivre’s Theorem and the *n*th-Root
Theorem **453**

*Chapter 7 Group Activity: Orbits of Planets*
**461**

*Chapter 7 Review* **463**

*Cumulative Review Exercise, Chapters 1–7*
467

**Appendix A COMMENTS ON NUMBERS 473**

**A.1** Real Numbers **474**

**A.2** Complex Numbers **477**

**A.3** Significant Digits **481**

**Appendix B FUNCTIONS AND INVERSE FUNCTIONS 489**

**B.1** Functions **490**

**B.2** Graphs and Transformations **497**

**B.3** Inverse Functions **508**

**Appendix C PLANE GEOMETRY: SOME USEFUL FACTS 515**

**C.1** Lines and Angles **516**

**C.2** Triangles **517**

**C.3** Quadrilaterals **519**

**C.4** Circles **520**

*Selected Answers* A-1

*Index* I-1