1 Right Triangle Trigonometry 2 1.1 Angles, Degrees, and Triangles 4 1.2 Similar Triangles 17 1.3 Definition 1 of Trigonometric Functions: Right Triangle Ratios 28 1.4 Evaluating Trigonometric Functions: Exactly and with Calculators 38 1.5 Solving Right Triangles 49 Inquiry-Based Learning Project 63 Modeling Our World 65 Review 67 Review Exercises 70 Practice Test 73 2 Trigonometric Functions 74 2.1 Angles in the Cartesian Plane 76 2.2 Definition 2 of Trigonometric Functions: The Cartesian Plane 84 2.
3 Evaluating Trigonometric Functions for Nonacute Angles 93 2.4 Basic Trigonometric Identities 110 Inquiry-Based Learning Project 120 Modeling Our World 121 Review 122 Review Exercises 124 Practice Test 126 Cumulative Test 127 3 Radian Measure and the Unit Circle Approach 128 3.1 Radian Measure 130 3.2 Arc Length and Area of a Circular Sector 141 3.3 Linear and Angular Speeds 151 3.4 Definition 3 of Trigonometric Functions: Unit Circle Approach 159 Inquiry-Based Learning Project 170 Modeling Our World 171 Review 172 Review Exercises 174 Practice Test 176 Cumulative Test 177 4 Graphing Trigonometric Functions 178 4.1 Basic Graphs of Sine and Cosine Functions: Amplitude and Period 180 4.2 Translations of the Sine and Cosine Functions: Addition of Ordinates 204 4.
3 Graphs of Tangent, Cotangent, Secant, and Cosecant Functions 226 Inquiry-Based Learning Project 246 Modeling Our World 247 Review 248 Review Exercises 251 Practice Test 254 Cumulative Test 255 5 Trigonometric Identities 256 5.1 Trigonometric Identities 258 5.2 Sum and Difference Identities 268 5.3 Double-Angle Identities 281 5.4 Half-Angle Identities 290 5.5 Product-to-Sum and Sum-to-Product Identities 300 Inquiry-Based Learning Project 309 Modeling Our World 310 Review 311 Review Exercises 313 Practice Test 316 Cumulative Test 317 6 Solving Trigonometric Equations 318 6.1 Inverse Trigonometric Functions 320 6.2 Solving Trigonometric Equations That Involve Only One Trigonometric Function 342 6.
3 Solving Trigonometric Equations That Involve Multiple Trigonometric Functions 353 Inquiry-Based Learning Project 360 Modeling Our World 362 Review 363 Review Exercises 366 Practice Test 368 Cumulative Test 369 7 Applications of Trigonometry: Triangles and Vectors 370 7.1 Oblique Triangles and the Law of Sines 372 7.2 The Law of Cosines 387 7.3 The Area of a Triangle 397 7.4 Vectors 405 7.5 The Dot Product 421 Inquiry-Based Learning Project 429 Modeling Our World 430 Review 431 Review Exercises 433 Practice Test 436 Cumulative Test 437 8 Complex Numbers, Polar Coordinates, and Parametric Equations 438 8.1 Complex Numbers 440 8.2 Polar (Trigonometric) Form of Complex Numbers 447 8.
3 Products, Quotients, Powers, and Roots of Complex Numbers: De Moivre?s Theorem 456 8.4 Polar Equations and Graphs 469 8.5 Parametric Equations and Graphs 483 Inquiry-Based Learning Project 494 Modeling Our World 495 Review 497 Review Exercises 499 Practice Test 501 Cumulative Test 502 Appendix A Algebraic Prerequisites and Review 503 A.1 Factoring Polynomials 504 A.2 Basic Tools: Cartesian Plane, Distance, and Midpoint 515 A.3 Graphing Equations: Point-Plotting, Intercepts, and Symmetry 523 A.4 Functions 535 A.5 Graphs of Functions; Piecewise-Defined Functions; Increasing and Decreasing Functions; Average Rate of Change 554 A.
6 Graphing Techniques: Transformations 574 A.7 Operations on Functions and Composition of Functions 589 A.8 One-to-One Functions and Inverse Functions 599 Review 614 Review Exercises 617 Practice Test 621 Appendix B Conic Sections 623 B.1 Conic Basics 624 B.2 The Parabola 627 B.3 The Ellipse 640 B.4 The Hyperbola 652 B.5 Rotation of Axes 664 B.
6 Polar Equations of Conics 674 Review 685 Review Exercises 688 Practice Test 691 Answers to Odd Numbered Exercises 692 Applications Index 738 Subject Index 740.