Table of Contents
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 TrigonometricFunctions 121
3.1 Basic Graphs 123
3.2 Graphing y = k + A sin Bx and y = k + A cos Bx 138
3.3 Graphing y = k + A sin (Bx + C) and y = k + A cos (Bx + C) 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 M sin Bt + N cos Bt to A sin(Bt + C) 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: sin 1/x = 0 and sin-1 1/x = 0 336
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
