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Analytic Trigonometry with Applications, 10th Edition
by
Barnett, Raymond A., Merritt College; Ziegler, Michael R., Marquette University; Byleen, Karl E., Marquette University
Publisher: John Wiley & Sons
Publishing Date: 2008/11/17
eText ISBN-10
0-470-41526-6
eText ISBN-13
978-0-470-41526-9
Print ISBN-10
0-470-28076-X
Print ISBN-13
978-0-470-28076-8
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Analytic Trigonometry with Applications, 10th Edition
by
Barnett, Raymond A., Merritt College; Ziegler, Michael R., Marquette University; Byleen, Karl E., Marquette University
eTextbook $80.50
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Copyright, iv
Preface, v
A Note on Calculators, xv
1. RIGHT TRIANGLE RATIOS,...
2. TRIGONOMETRIC FUNCTION...
3. GRAPHING TRIGONOMETRIC...
4. IDENTITIES, 229
5. INVERSE TRIGONOMETRIC ...
6. ADDITIONAL TOPICS: TRI...
7. POLAR COORDINATES; COM...
Appendix A. COMMENTS ON N...
Appendix B. FUNCTIONS AND...
Appendix C. PLANE GEOMETR...
Selected Answers, A-1
Index, I-1
Table of Contents
Copyright, iv
Preface, v
A Note on Calculators, xv
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, 66
2.3. Trigonometric Functions: Unit Circle Approach, 73
2.4. Additional Applications, 85
2.5. Exact Values and Properties of Trigonometric Functions, 99
Chapter 2 Group Activity: Speed of Light in Water, 114
Chapter 2 Review, 116
3. GRAPHING TRIGONOMETRIC FUNCTIONS, 123
3.1. Basic Graphs, 125
3.2. Graphing y =
k + A
sin
Bx
and y =
k + A
cos
Bx
, 140
3.3. Graphing y =
k + A
sin(
Bx + C
) and y =
k + A
cos(
Bx + C
), 159
3.4. Additional Applications, 174
3.5. Graphing Combined Forms, 190
3.6. Tangent, Cotangent, Secant, and Cosecant Functions Revisited, 202
Chapter 3 Group Activity: Predator–Prey Analysis Involving Coyotes and Rabbits, 213
Chapter 3 Review, 215
Cumulative Review Exercise, Chapters 1–3, 223
4. IDENTITIES, 229
4.1. Fundamental Identities and Their Use, 230
4.2. Verifying Trigonometric Identities, 237
4.3. Sum, Difference, and Cofunction Identities, 247
4.4. Double-Angle and Half-Angle Identities, 258
4.5. Product–Sum and Sum–Product Identities, 269
Chapter 4 Group Activity: From M
sin
Bt + N
cos
Bt to A
sin(Bt + C), 277
Chapter 4 Review, 279
5. INVERSE TRIGONOMETRIC FUNCTIONS; TRIGONOMETRIC EQUATIONS AND INEQUALITIES, 287
5.1. Inverse Sine, Cosine, and Tangent Functions, 288
5.2. Inverse Cotangent, Secant, and Cosecant Functions, 309
5.3. Trigonometric Equations: An Algebraic Approach, 315
5.4. Trigonometric Equations and Inequalities: A Graphing Calculator Approach, 329
Chapter 5 Group Activity:
sin 1/x=0
and
sin
-1
1/x =0, 338
Chapter 5 Review, 339
Cumulative Review Exercise, Chapters 1–5, 345
6. ADDITIONAL TOPICS: TRIANGLES AND VECTORS, 351
6.1. Law of Sines, 352
6.2. Law of Cosines, 367
6.3. Areas of Triangles, 378
6.4. Vectors: Geometrically Defined, 385
6.5. Vectors: Algebraically Defined, 396
6.6. The Dot Product, 410
Chapter 6 Group Activity: The SSA Case and the Law of Cosines, 420
Chapter 6 Review, 421
7. POLAR COORDINATES; COMPLEX NUMBERS, 431
7.1. Polar and Rectangular Coordinates, 432
7.2. Sketching Polar Equations, 440
7.3. The Complex Plane, 453
7.4. De Moivre’s Theorem and the
n
th-Root Theorem, 462
Chapter 7 Group Activity: Orbits of Planets, 469
Chapter 7 Review, 471
Cumulative Review Exercise, Chapters 1–7, 475
Appendix A. COMMENTS ON NUMBERS, 481
A.1. Real Numbers, 482
A.2. Complex Numbers, 485
A.3. Significant Digits, 489
Appendix B. FUNCTIONS AND INVERSE FUNCTIONS, 497
B.1. Functions, 498
B.2. Graphs and Transformations, 505
B.3. Inverse Functions, 516
Appendix C. PLANE GEOMETRY: SOME USEFUL FACTS, 523
C.1. Lines and Angles, 524
C.2. Triangles, 525
C.3. Quadrilaterals, 527
C.4. Circles, 528
Selected Answers, A-1
Index, I-1
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