Trigonometry

Trigonometry focuses on the principles, operations, formulas, and functions involved in trigonometry.

The publication first takes a look at the six trigonometric functions, right triangle trigonometry, and radian measure. Discussions focus on radiance and degrees, unit circle and even and odd functions, length of arc and area of a sector, trigonometric functions of an acute angle, solving right triangles, rectangular coordinate system, and angles, degrees, and special triangles. The manuscript then examines graphing and inverse functions, identities and formulas, and equations. Topics include solving trigonometric equations, parametric equations and further graphing, sum and difference formulas, half-angle formulas, additional identities, phase shift, amplitude and period, graphing combinations of functions, and inverse trigonometric functions. The text ponders on complex numbers and polar coordinates, triangles, and equations, including the law of sines and cosines, products and quotients in trigonometric form, roots of a complex number, and polar coordinates.

The book is a dependable reference for students and readers interested in trigonometry.

1 The Six Trigonometric Functions I

1.1 Angles, Degrees, and Special Triangles

1.2 The Rectangular Coordinate System

1.3 Definition 1: Trigonometric Functions

1.4 Introduction to Identities

1.5 More Identities

Summary and Review

Test

2 Right Triangle Trigonometry

2.1 Trigonometric Functions of an Acute Angle

2.2 Tables and Calculators for Trigonometric Functions of an Acute Angle

2.3 Solving Right Triangles

2.4 Applications

2.5 Vectors

Summary and Review

Test

3 Radian Measure

3.1 Reference Angle

3.2 Radians and Degrees

3.3 The Unit Circle and Even and Odd Functions

3.4 Length of Arc and Area of a Sector

3.5 Velocities

Summary and Review

Test

4 Graphing and Inverse Functions

4.1 Basic Graphs

4.2 Amplitude and Period

4.3 Phase Shift

4.4 Graphing Combinations of Functions

4.5 Inverse Trigonometric Relations

4.6 Inverse Trigonometric Functions

Summary and Review

Test

5 Identities and Formulas

5.1 Proving Identities

5.2 Sum and Difference Formulas

5.3 Double-Angle Formulas

5.4 Half-Angle Formulas

5.5 Additional Identities

Summary and Review

Test

6 Equations

6.1 Solving Trigonometric Equations

6.2 More on Trigonometric Equations

6.3 Trigonometric Equations Involving Multiple Angles

6.4 Parametric Equations and Further Graphing

Summary and Review

Test

7 Triangles

7.1 The Law of Sines

7.2 The Ambiguous Case

7.3 The Law of Cosines

7.4 The Area of a Triangle

Summary and Review

Test

8 Complex Numbers and Polar Coordinates

8.1 Complex Numbers

8.2 Trigonometric Form for Complex Numbers

8.3 Products and Quotients in Trigonometric Form

8.4 Roots of a Complex Number

8.5 Polar Coordinates

8.6 Equations in Polar Coordinates and Their Graphs

Summary and Review

Test

Appendix: Logarithms

A.1 Logarithms Are Exponents

A.2 Common Logarithms and Computations

A.3 Exponential Equations, Logarithmic Equations, and Change of Base

A.4 Word Problems

Tables

Table I: Powers, Roots, and Prime Factors

Table II: Trigonometric Functions—Decimal Degrees

Table III: Trigonometric Functions—Degrees and Minutes

Table IV: Common Logarithms

Answers to Odd-Numbered Problems and Chapter Tests

Index