Trigonometry

Copyright......Page 6
About the Author......Page 9
Preface......Page 10
Trigonometry......Page 5
Table of Contents......Page 18
A Note from the Author to the Student......Page 21
1: Right Triangle Trigonometry......Page 30
1.1: Angles, Degrees, and Triangles......Page 32
1.2: Similar Triangles......Page 45
1.3: Definition 1 of Trigonometric Functions: Right Triangle Ratios......Page 56
1.4: Evaluating Trigonometric Functions: Exactly and with Calculators......Page 66
1.5: Solving Right Triangles......Page 77
Inquiry-Based Learning Project......Page 91
Modeling Our World......Page 93
Review......Page 95
Review Exercises......Page 98
Practice Test......Page 101
2: Trigonometric Functions......Page 102
2.1: Angles in the Cartesian Plane......Page 104
2.2: Definition 2 of Trigonometric Functions: The Cartesian Plane......Page 112
2.3: Evaluating Trigonometric Functions for Nonacute Angles......Page 121
2.4: Basic Trigonometric Identities......Page 138
Inquiry-Based Learning Project......Page 148
Modeling Our World......Page 149
Review......Page 150
Review Exercises......Page 152
Practice Test......Page 154
Cumulative Test......Page 155
3: Radian Measure and the Unit Circle Approach......Page 156
3.1: Radian Measure......Page 158
3.2: Arc Length and Area of a Circular Sector......Page 169
3.3: Linear and Angular Speeds......Page 179
3.4: Definition 3 of Trigonometric Functions: Unit Circle Approach......Page 187
Inquiry-Based Learning Project......Page 198
Modeling Our World......Page 199
Review......Page 200
Review Exercises......Page 202
Practice Test......Page 204
Cumulative Test......Page 205
4: Graphing Trigonometric Functions......Page 206
4.1: Basic Graphs of Sine and Cosine Functions: Amplitude and Period......Page 208
4.2: Translations of the Sine and Cosine Functions: Addition of Ordinates......Page 232
4.3: Graphs of Tangent, Cotangent, Secant, and Cosecant Functions......Page 254
Inquiry-Based Learning Project......Page 274
Modeling Our World......Page 275
Review......Page 276
Review Exercises......Page 279
Practice Test......Page 282
Cumulative Test......Page 283
5: Trigonometric Identities......Page 284
5.1: Trigonometric Identities......Page 286
5.2: Sum and Difference Identities......Page 296
5.3: Double-Angle Identities......Page 309
5.4: Half-Angle Identities......Page 318
5.5: Product-to-Sum and Sum-to-Product Identities......Page 328
Inquiry-Based Learning Project......Page 337
Modeling Our World......Page 338
Review......Page 339
Review Exercises......Page 341
Practice Test......Page 344
Cumulative Test......Page 345
6: Solving Trigonometric Equations......Page 346
6.1: Inverse Trigonometric Functions......Page 348
6.2: Solving Trigonometric Equations That Involve Only One Trigonometric Function......Page 370
6.3: Solving Trigonometric Equations That Involve Multiple Trigonometric Functions......Page 381
Inquiry-Based Learning Project......Page 388
Modeling Our World......Page 390
Review......Page 391
Review Exercises......Page 394
Practice Test......Page 396
Cumulative Test......Page 397
7: Applications of Trigonometry: Triangles and Vectors......Page 398
7.1: Oblique Triangles and the Law of Sines......Page 400
7.2: The Law of Cosines......Page 415
7.3: The Area of a Triangle......Page 425
7.4: Vectors......Page 433
7.5: The Dot Product......Page 449
Inquiry-Based Learning Project......Page 457
Modeling Our World......Page 458
Review......Page 459
Review Exercises......Page 461
Practice Test......Page 464
Cumulative Test......Page 465
8: Complex Numbers, Polar Coordinates, and Parametric Equations......Page 466
8.1: Complex Numbers......Page 468
8.2: Polar (Trigonometric) Form of Complex Numbers......Page 475
8.3: Products, Quotients, Powers, and Roots of Complex Numbers: De Moivre's Theorem......Page 484
8.4: Polar Equations and Graphs......Page 497
8.5: Parametric Equations and Graphs......Page 511
Inquiry-Based Learning Project......Page 522
Modeling Our World......Page 523
Review......Page 525
Review Exercises......Page 527
Practice Test......Page 529
Cumulative Test......Page 530
Appendix A: Algebraic Prerequisites and Review......Page 531
A.1: Factoring Polynomials......Page 532
A.2: Basic Tools: Cartesian Plane, Distance, and Midpoint......Page 543
A.3: Graphing Equations: Point-Plotting, Intercepts, and Symmetry......Page 551
A.4: Functions......Page 563
A.5: Graphs of Functions; Piecewise-Defined Functions; Increasing and Decreasing Functions; Average Rate of Change......Page 582
A.6: Graphing Techniques: Transformations......Page 602
A.7: Operations on Functions and Composition of Functions......Page 617
A.8: One-to-One Functions and Inverse Functions......Page 627
Review......Page 642
Review Exercises......Page 645
Practice Test......Page 649
Appendix B: Conic Sections......Page 651
B.1: Conic Basics......Page 652
B.2: The Parabola......Page 655
B.3: The Ellipse......Page 668
B.4: The Hyperbola......Page 680
B.5: Rotation of Axes......Page 692
B.6: Polar Equations of Conics......Page 702
Review......Page 713
Review Exercises......Page 716
Practice Test......Page 719
Answers to Odd Numbered Exercises......Page 720
Applications Index......Page 766
Subject Index......Page 768