Analytic Trigonometry with Applications

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 nth-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