Trigonometry

Cover......Page 1
Contents......Page 7
Preface......Page 10
Instructor Resources......Page 13
Student Resources......Page 14
Acknowledgments......Page 15
Ch P: Prerequisites......Page 17
P.1 Review of Real Numbers and Their Properties......Page 18
P.2 Solving Equations......Page 30
P.3 The Cartesian Plane and Graphs of Equations......Page 42
P.4 Linear Equations in Two Variables......Page 56
P.5 Functions......Page 69
P.6 Analyzing Graphs of Functions......Page 83
P.7 A Library of Parent Functions......Page 94
P.8 Transformations of Functions......Page 101
P.9 Combinations of Functions: Composite Functions......Page 110
P.10 Inverse Functions......Page 118
Chapter Summary......Page 127
Review Exercises......Page 130
Chapter Test......Page 133
Proofs in Mathematics......Page 134
P.S. Problem Solving......Page 135
Ch 1: Trigonometry......Page 137
1.1 Radian and Degree Measure......Page 138
1.2 Trigonometric Functions: The Unit Circle......Page 148
1.3 Right Triangle Trigonometry......Page 155
1.4 Trigonometric Functions of Any Angle......Page 166
1.5 Graphs of Sine and Cosine Functions......Page 175
1.6 Graphs of Other Trigonometric Functions......Page 186
1.7 Inverse Trigonometric Functions......Page 196
1.8 Applications and Models......Page 206
Chapter Summary......Page 216
Review Exercises......Page 218
Chapter Test......Page 221
Proofs in Mathematics......Page 222
P.S. Problem Solving......Page 223
Ch 2: Analytic Trigonometry......Page 225
2.1 Using Fundamental Identities......Page 226
2.2 Verifying Trigonometric Identities......Page 233
2.3 Solving Trigonometric Equations......Page 240
2.4 Sum and Difference Formulas......Page 252
2.5 Multiple-Angle and Product-to-Sum Formulas......Page 259
Chapter Summary......Page 268
Review Exercises......Page 270
Chapter Test......Page 272
Proofs in Mathematics......Page 273
P.S. Problem Solving......Page 275
Ch 3: Additional Topics in Trigonometry......Page 277
3.1 Law of Sines......Page 278
3.2 Law of Cosines......Page 287
3.3 Vectors in the Plane......Page 294
3.4 Vectors and Dot Products......Page 307
Chapter Summary......Page 316
Review Exercises......Page 318
Chapter Test......Page 321
Cumulative Test for Chapters 1-3......Page 322
Proofs in Mathematics......Page 324
P.S. Problem Solving......Page 327
Ch 4: Complex Numbers......Page 329
4.1 Complex Numbers......Page 330
4.2 Complex Solutions of Equations......Page 337
4.3 The Complex Plane......Page 345
4.4 Trigonometric Form of a Complex Number......Page 352
4.5 DeMoivre's Theorem......Page 358
Chapter Summary......Page 364
Review Exercises......Page 366
Chapter Test......Page 369
Proofs in Mathematics......Page 370
P.S. Problem Solving......Page 371
Ch 5: Exponential and Logarithmic Functions......Page 373
5.1 Exponential Functions and Their Graphs......Page 374
5.2 Logarithmic Functions and Their Graphs......Page 385
5.3 Properties of Logarithms......Page 395
5.4 Exponential and Logarithmic Equations......Page 402
5.5 Exponential and Logarithmic Models......Page 412
Chapter Summary......Page 424
Review Exercises......Page 426
Chapter Test......Page 429
Proofs in Mathematics......Page 430
P.S. Problem Solving......Page 431
Ch 6: Topics in Analytic Geometry......Page 433
6.1 Lines......Page 434
6.2 Introduction to Conics: Parabolas......Page 441
6.3 Ellipses......Page 450
6.4 Hyperbolas......Page 459
6.5 Rotation of Conics......Page 469
6.6 Parametric Equations......Page 477
6.7 Polar Coordinates......Page 487
6.8 Graphs of Polar Equations......Page 493
6.9 Polar Equations of Conics......Page 501
Chapter Summary......Page 508
Review Exercises......Page 510
Chapter Test......Page 513
Cumulative Test for Chapters 4-6......Page 514
Proofs in Mathematics......Page 516
P.S. Problem Solving......Page 519
Answers to Odd-Numbered Exercises and Tests......Page 521
Index......Page 593