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Tables of Contents for Plane Trigonometry
Chapter/Section Title
Page #
Page Count
Some Fundamental Concepts
1
61
Calculators and Computations
2
7
The Rectangular Coordinate System
9
6
Functions
15
8
The Graph of a Function
23
12
The Graphing Calculator
35
6
Angles
41
8
Some Facts About Triangles
49
13
The Trigonometric Functions
62
31
Definitions of the Trigonometric Functions
62
8
Fundamental Relations
70
5
The Values of the Trigonometric Functions for Special Angles
75
4
Reference Angles
79
4
Finding Values of Trigonometric Functions with a Calculator
83
10
The Solution of Triangles
93
56
Solving Right Triangles
93
12
Oblique Triangles: The Law of Cosines
105
8
Oblique Triangles: The Law of Sines
113
6
The Ambiguous Case
119
5
Analysis of the General Triangle
124
1
Vectors
125
7
Applications of Vectors
132
9
Area Formulas
141
8
Radian Measure
149
18
The Radian
149
6
Arc Length and the Area of a Sector
155
5
Angular and Linear Velocity
160
7
Analytic Trigonometry
167
62
Trigonometric Functions of Real Numbers
167
7
Analytic Properties of the Sine and Cosine Functions
174
13
Expansion and Contraction of Sine and Cosine Graphs
187
9
Vertical and Horizontal Translation
196
9
Sinusoidal Modeling
205
8
Addition of Ordinates
213
4
Graphs of the Tangent and Cotangent Functions
217
3
Graphs of the Secant and Cosecant Functions
220
3
A Fundamental Inequality
223
6
Identities, Equations, and Inequalities
229
34
Fundamental Trigonometric Relations
229
6
Trigonometric Identities
235
8
Trigonometric Equations
243
6
Parametric Equations
249
5
Graphical Solutions of Trigonometric Equations and Inequalities
254
9
Composite Angle Identities
263
27
The Cosine of the Difference or Sum of Two Angles
263
7
Other Addition Formulas
270
5
Double-and Half-Angle Formulas
275
8
Sum and Product Formulas
283
7
The Inverse Trigonometric Functions
290
22
Relations, Functions, and Inverses
290
7
The Inverse Trigonometric Functions
297
7
Graphs of the Inverse Trigonometric Functions
304
8
Complex Numbers and Polar Equations
312
21
Complex Numbers
312
4
Polar Representation of Complex Numbers
316
5
DeMoivre's Theorem
321
4
Polar Equations and Their Graphs
325
8
Exponential and Logarithmic Functions
333
23
Exponential Functions
333
8
The Logarithm Function
341
6
Basic Properties of Logarithms
347
3
Exponential and Logarithmic Equations
350
6
Analytic Geometry
356
43
Lines
356
9
The Parabola
365
6
The Ellipse and the Circle
371
7
The Hyperbola
378
5
Translation of Axes
383
4
Rotation of Axes
387
4
The General Second-Degree Equation
391
8
APPENDIX A Calculators
399
20
A.1 Arithmetic Operations
399
2
A.2 Operating Systems and Memory
401
4
A.3 Scientific Notation
405
4
APPENDIX B Review of Elementary Geometry
409
1
B.1 Angles
409
2
B.2 Intersection of Lines
411
1
B.3 Polygons
411
2
B.4 Triangles
413
3
B.5 Quadrilaterals
416
1
B.6 Circles
416
1
B.7 Formulas from Geometry
417
2
Answers to Odd-Numbered Exercises
419
54
Index
473