Contents

CHAPTER 1 Angles and Applications

1.1 Introduction

1.2 Plane Angle

1.3 Measures of Angles

1.4 Arc Length

1.5 Lengths of Arcs on a Unit Circle

1.6 Area of a Sector

1.7 Linear and Angular Velocity

CHAPTER 2 Trigonometric Functions of a General Angle

2.1 Coordinates on a Line

2.2 Coordinates in a Plane

2.3 Angles in Standard Position

2.4 Trigonometric Functions of a General Angle

2.5 Quadrant Signs of the Functions

2.6 Trigonometric Functions of Quadrantal Angles

2.7 Undefined Trigonometric Functions

2.8 Coordinates of Points on a Unit Circle

2.9 Circular Functions

CHAPTER 3 Trigonometric Functions of an Acute Angle

3.1 Trigonometric Functions of an Acute Angle

3.2 Trigonometric Functions of Complementary Angles

3.3 Trigonometric Functions of 30°, 45°, and 60°

3.4 Trigonometric Function Values

3.5 Accuracy of Results Using Approximations

3.6 Selecting the Function in Problem-Solving

3.7 Angles of Depression and Elevation

CHAPTER 4 Solution of Right Triangles

4.1 Introduction

4.2 Four-Place Tables of Trigonometric Functions

4.3 Tables of Values for Trigonometric Functions

4.4 Using Tables to Find an Angle Given a Function Value

4.5 Calculator Values of Trigonometric Functions

4.6 Find an Angle Given a Function Value Using a Calculator

4.7 Accuracy in Computed Results

CHAPTER 5 Practical Applications

5.1 Bearing

5.2 Vectors

5.3 Vector Addition

5.4 Components of a Vector

5.5 Air Navigation

5.6 Inclined Plane

CHAPTER 6 Reduction to Functions of Positive Acute Angles

6.1 Coterminal Angles

6.2 Functions of a Negative Angle

6.3 Reference Angles

6.4 Angles with a Given Function Value

CHAPTER 7 Variations and Graphs of the Trigonometric Functions

7.1 Line Representations of Trigonometric Functions

7.2 Variations of Trigonometric Functions

7.3 Graphs of Trigonometric Functions

7.4 Horizontal and Vertical Shifts

7.5 Periodic Functions

7.6 Sine Curves

CHAPTER 8 Basic Relationships and Identities

8.1 Basic Relationships

8.2 Simplification of Trigonometric Expressions

8.3 Trigonometric Identities

CHAPTER 9 Trigonometric Functions of Two Angles

9.1 Addition Formulas

9.2 Subtraction Formulas

9.3 Double-Angle Formulas

9.4 Half-Angle Formulas

CHAPTER 10 Sum, Difference, and Product Formulas

10.1 Products of Sines and Cosines

10.2 Sum and Difference of Sines and Cosines

CHAPTER 11 Oblique Triangles

11.1 Oblique Triangles

11.2 Law of Sines

11.3 Law of Cosines

11.4 Solution of Oblique Triangles

CHAPTER 12 Area of a Triangle

12.1 Area of a Triangle

12.2 Area Formulas

CHAPTER 13 Inverses of Trigonometric Functions

13.1 Inverse Trigonometric Relations

13.2 Graphs of the Inverse Trigonometric Relations

13.3 Inverse Trigonometric Functions

13.4 Principal-Value Range

13.5 General Values of Inverse Trigonometric Relations

CHAPTER 14 Trigonometric Equations

14.1 Trigonometric Equations

14.2 Solving Trigonometric Equations

CHAPTER 15 Complex Numbers

15.1 Imaginary Numbers

15.2 Complex Numbers

15.3 Algebraic Operations

15.4 Graphic Representation of Complex Numbers

15.5 Graphic Representation of Addition and Subtraction

15.6 Polar or Trigonometric Form of Complex Numbers

15.7 Multiplication and Division in Polar Form

15.8 De Moivre’s Theorem

15.9 Roots of Complex Numbers

APPENDIX 1 Geometry

A1.1 Introduction

A1.2 Angles

A1.3 Lines

A1.4 Triangles

A1.5 Polygons

A1.6 Circles

APPENDIX 2 Tables

Table 1 Trigonometric Functions—Angle in 10-Minute Intervals

Table 2 Trigonometric Functions—Angle in Tenth of Degree Intervals

Table 3 Trigonometric Functions—Angle in Hundredth of Radian Intervals

INDEX