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Tables of Contents for Analytic Trigonometry With Applications
Chapter/Section Title
Page #
Page Count
A Note on Calculators
xix
Right Triangle Ratios
1
48
Angles, Degrees, and Arcs
2
11
Similar Triangles
13
7
Trigonometric Ratios and Right Triangles
20
11
Right Triangle Applications
31
18
Chapter 1 Group Activity: A Logistics Problem
41
1
Chapter 1 Review
42
7
Trigonometric Functions
49
78
Degrees and Radians
50
13
Linear and Angular Velocity
63
6
Trigonometric Functions
69
11
Additional Applications
80
13
Exact Value for Special Angles and Real Numbers
93
11
Circular Functions
104
23
Chapter 2 Group Activity: Speed of Light in Water
116
2
Chapter 2 Review
118
9
Graphing Trigonometric Functions
127
90
Basic Graphs
129
14
Graphing y = k + A sin Bx and y = k + A cos Bx
143
15
Graphing y = k + A sin(Bx + C) and y = k + A cos(Bx + C)
158
11
Additional Applications
169
14
Graphing Combined Forms
183
10
Tangent, Cotangent, Secant, and Cosecant Functions Revisited
193
24
Chapter 3 Group Activity: Predator--Prey Analysis Involving Coyotes and Rabbits
202
1
Chapter 3 Review
203
8
Cumulative Review Exercise
211
6
Identities
217
54
Fundamental Identities and Their Use
218
7
Verifying Trigonometric Identities
225
9
Sum, Difference, and Confunction Identities
234
10
Double-Angle and Half-Angle Identities
244
10
Product--Sum and Sum--Product Identities
254
17
Chapter 4 Group Activity: From M sin Bt + N cos Bt to A sin(Bt + C)
262
2
Chapter 4 Review
264
7
Inverse Trigonometric Functions; Trigonometric Equations and Inequalities
271
52
Inverse Sine, Cosine, and Tangent Functions
272
19
Inverse Cotangent, Secant, and Cosecant Functions
291
5
Trigonometric Equations: An Algebraic Approach
296
7
Trigonometric Equations and Inequalities: A Graphing Utility Approach
303
20
Chapter 5 Group Activity: sin 1/x = 0 and sin -1 1/x = 0
310
1
Chapter 5 Review
311
5
Cumulative Review Exercise
316
7
Additional Topics: Triangles and Vectors
323
70
Law of Sines
324
12
Law of Cosines
336
10
Areas of Triangles
346
5
Vectors: Geometrically Defined
351
8
Vectors: Algebraically Defined
359
12
The Dot Product
371
22
Chapter 6 Group Activity: The SSA Case and the Law of Cosines
381
1
Chapter 6 Review
382
11
Polar Coordinates; Complex Numbers
393
48
Polar and Rectangular Coordinates
394
8
Sketching Polar Equations
402
12
Complex Numbers in Rectangular and Polar Forms
414
8
De Moivre's Theorem and the nth-Root Theorem
422
19
Chapter 7 Group Activity: Orbits of Planets
428
2
Chapter 7 Review
430
4
Cumulative Review Exercise
434
7
Appendix A COMMENTS ON NUMBERS
441
15
A.1 Real Numbers
442
3
A.2 Complex Numbers
445
4
A.3 Significant Digits
449
7
Appendix B FUNCTIONS AND INVERSE FUNCTIONS
456
16
B.1 Functions
457
7
B.2 Inverse Functions
464
8
Appendix C PLANE GEOMETRY: SOME USEFUL FACTS
472
C.1 Lines and Angles
473
C.2 Triangles
474
C.3 Quadrilaterals
476
C.4 Circles
477
Selected Answers
A-1
Index
I-1
Applications Index
i