CHAPTER 1: The Trigonometric Functions

1.1 Historical Overview

1.2 The Rectangular Coordinate System

1.3 The Distance Formula

Exercise 1.1

1.4 Trigonometric Angles

Exercise 1.2

1.5 Definitions of the Trigonometric Functions of a General Angle

Exercise 1.3

1.6 Consequences of the Definitions

Exercise 1.4

1.7 Given One Trigonometric Function of an Angle, to Draw the Angle and Find the Other Functions

Exercise 1.5

1.8 Trigonometric Functions of an Acute Angle

Exercise 1.6

1.9 Cofunctions

1.10 The Trigonometric Functions of 30°, 45°, 60°

Exercise 1.7

Key Terms, Review Exercises

CHAPTER 2: Trigonometric Functions of any Angle

2.1 Hand Calculators

2.2 Approximations and Significant Figures

Exercise 2.1

2.3 Two Problems

Exercise 2.2

2.4 Related Angles

2.5 Reduction to Functions of an Acute Angle

Exercise 2.3

2.6 Trigonometric Functions of the Negative of an Angle

Exercise 2.4

Key Terms, Review Exercises

CHAPTER 3: Solving Triangles and Applications

3.1 The Solution of Right Triangles

Exercise 3.1

3.2 Angles of Elevation and Depression; Bearing of a Line

Exercise 3.2

3.3 Vectors

Exercise 3.3

3.4 Oblique Triangles

3.5 The Law of Sines

3.6 Applications of the Law of Sines: SAA

Exercise 3.4

3.7 The Ambiguous Case: SSA

Exercise 3.5

3.8 The Law of Cosines

3.9 Applications of the Law of Cosines: SAS and SSS

Exercise 3.6

3.10 The Area of a Triangle

Exercise 3.7

Key Terns, Review Exercises

CHAPTER 4: Radian Measure

4.1 The Radian

Exercise 4.1

4.2 Length of a Circular Arc

4.3 The Wrapping Function

4.4 The Circular Functions

Exercise 4.2

4.5 Linear and Angular Velocity

Exercise 4.3

Key Terms, Reviewer Exercises

CHAPTER 5: Trigonometric Identities

5.1 The Fundamental Relations

Exercise 5.1

5.2 Algebraic Operations with the Trigonometric Functions

Exercise 5.2

5.3 Identities and Conditional Equations

5.4 Trigonometric Identities

Exercise 5.3

Key Terms, Review Exercises

CHAPTER 6: Functions of Two Angles

6.1 Functions of the Sum of Two Angles

Exercise 6.1

6.2 tan(A + B)

6.3 Reduction of a sin Ø + b cos Ø to k sin(Ø + H)

Exercise 6.2

6.4 Double-Angle Formulas

6.5 Half-Angle Formulas

Exercise 6.3

6.6 Product-to-Sum Formulas; Sum-to-Product Formulas

Exercise 6.4

Key Terms, Review Exercises

CHAPTER 7: Trigonometric Equations

7.1 Conditional Trigonometric Equations

7.2 Solving a Trigonometric Equation Algebraically

Exercise 7.1

Key Terms, Review Exercises

CHAPTER 8: Graphs of the Trigonometric Functions

8.1 Periodic Functions

8.2 Graphs of the Trigonometric Functions

Exercise 8.1

8.3 The Graph y = a sin(bx + c)

8.4 Sketching Curves by Composition of y Coordinates

8.5 The Graph of y = a sin x + b cos x

Exercise 8.2

8.6 Using Graphing Calculators

Exercise 8.3

Key Terms, Review Exercises

CHAPTER 9: Inverse Trigonometric Functions

9.1 Inverse Functions

Exercise 9.1

9.2 Inverse Trigonometric Functions

Exercise 9.2

9.3 Operations Involving Inverse Trigonometric Functions

Exercise 9.3

Key Terms, Review Exercises

CHAPTER 10: Transcendental Functions

10.1 The Logarithm Function

Exercise 10.1

10.2 The Exponential Function

Exercise 10.2

10.3 Logarithmic and Exponential Equations

Exercise 10.3

Key Terms, Review Exercises

CHAPTER 11: Polar Coordinates

11.1 Parametric Equations

Exercise 11.1

11.2 Polar Coordinates

Exercise 11.2

11.3 Graphing in Polar Coordinates

Exercise 11.3

Key Terms, Review Exercises

CHAPTER 12: Complex Numbers

12.1 Complex Numbers

Exercise 12.1

12.2 Graphical Representation of Complex Numbers

12.3 Polar Form of a Complex Number

Exercise 12.2

12.4 Multiplication of Complex Numbers in Polar Form

12.5 DeMoivre's Theorem

Exercise 12.3

Key Terms, Review Exercises

CHAPTER 13: Topics From Analytic Geometry

13.1 Straight Lines

Exercise 13.1

13.2 The Parabola

Exercise 13.2

13.3 The Ellipse

Exercise 13.3

Key Terms, Review Exercises

Appendix

A.1 Circular and Exponential Functions

Exercise A.1

A.2 Hyperbolic Trigonometric Functions

Exercise A.2

A.3 Change of Base of Logarithms

Exercise A.3

A.4 Using a Table of Trigonometric Functions

Exercise A.4

A.5 Interpolation

Exercise A.5

Answers

Table

Values of the Trigonometric Functions to Four Places

Index