Preface xi
Chapter 1 Circular Functions 1
1.1 Fundamentals for Trigonometry 2
1.2 Circular Functions: The Cosine and Sine Functions 4
1.3 Functional Values for Common Arcs 16
1.4 Reference Arcs and Functional Values for cos x and sin x, x 27
1.5 Four Additional Circular Functions: Tangent, Secant, Cosecant, and Cotangent Functions 40
1.6 Negative Identities and Periods for the Circular Functions 53
Chapter Summary 63
Review Exercises 66
Chapter Test 71
Chapter 2 Graphs of the Circular Functions 73
2.1 Graphs of the Sine and Cosine Functions 74
2.2 Period, Phase Shift, and Other Translations 92
2.3 Applications and Modeling with Sinusoidal Functions 109
2.4 Graphs of the Tangent, Cotangent, Secant, and Cosecant Functions 119
2.5 Inverses of the Circular Functions 133Chapter Summary 147
Review Exercises 151
Chapter Test 155
Chapter 3 The Trigonometric Functions 159
3.1 Angles and Their Measure 160
3.2 Trigonometric and Circular Functions 173
3.3 Solving Right Triangles and Applications 185
3.4 Solution of Triangles Using Law of Sines 204
3.5 Solution of Triangles Using Law of Cosines 218
Chapter Summary 227
Review Exercises 230
Chapter Test 233
Chapter 4 Identities 235
4.1 Proving Identities 236
4.2 Sum and Difference Identities for Cosine 248
4.3 Sum and Difference Identities for Sine and Tangent 258
4.4 Double-Angle Identities 266
4.5 Half-Angle and Additional Identities 273Chapter Summary 284
Review Exercises 286
Chapter Test 289
Chapter 5 Trigonometric Equations 291
5.1 Solving Conditional Equations I 292
5.2 Solving Trigonometric Conditional Equations II 298
5.3 More Trigonometric Equations, Multiple-Angle Equations 304
5.4 Parametric Equations 313
Chapter Summary 322
Review Exercises 323
Chapter Test 325
Chapter 6 Vectors, Polar Equations, and Complex Numbers 327
6.1 Geometric Vectors and Applications 328
6.2 Algebraic Vectors 339
6.3 Polar Coordinate System 350
6.4 Complex Numbers 364
6.5 Trigonometric Form for Complex Numbers 372
Chapter Summary 385
Review Exercises 389
Chapter Test 391
Cumulative Review 393
Appendix A Algebra Review 399
Appendix B Geometry Review 425
Answers to Selected Exercises A-1
Index I-1