Table of Contents

 

Table of Contents

Preface

Resources for Success

 

R. Algebra Review 

R.1 Basic Concepts from Algebra 

R.2 Real Number Operations and Properties 

R.3 Exponents, Polynomials, and Factoring 

R.4 Rational Expressions 

R.5 Radical Expressions 

R.6 Equations and Inequalities 

R. 7 Rectangular Coordinates and Graphs 

R.8 Functions 

R.9 Graphing Techniques 

1. Trigonometric Functions

1-1 Angles

1-2 Angle Relationships and Similar Triangles

1-3 Trigonometric Functions

1-4 Using the Definitions of the Trigonometric Functions

Test Prep

Review Exercises

Test

2. Acute Angles and Right Triangles

2-1 Trigonometric Functions of Acute Angles

2-2 Trigonometric Functions of Non-Acute Angles

2-3 Approximations of Trigonometric Function Values

2-4 Solutions and Applications of Right Triangles

2-5 Further Applications of Right Triangles

Test Prep

Review Exercises

Test

3. Radian Measure and the Unit Circle

3-1 Radian Measure

3-2 Applications of Radian Measure

3-3 The Unit Circle and Circular Functions

3-4 Linear and Angular Speed

Test Prep

Review Exercises

Test

4. Graphs of the Circular Functions

4-1 Graphs of the Sine and Cosine Functions

4-2 Translations of the Graphs of Sine and Cosine Functions

4-3 Graphs of the Tangent and Cotangent Functions

4-4 Graphs of the Secant and Cosecant Functions

4-5 Harmonic Motion

Test Prep

Review Exercises

Test

5. Trigonometric Identities

5-1 Fundamental Identities

5-2 Verifying Trigonometric Identities

5-3 Sum and Difference Identities for Cosine

5-4 Sum and Difference Identities for Sine and Tangent

5-5 Double-Angle Identities

5-6 Half-Angle Identities

Test Prep

Review Exercises

Test

6. Inverse Circular Functions and Trigonometric Equations

6-1 Inverse Circular Functions

6-2 Trigonometric Equations I

6-3 Trigonometric Equations II

6-4 Equations Involving Inverse Trigonometric Functions

Test Prep

Review Exercises

Test

7. Applications of Trigonometry and Vectors

7-1 Oblique Triangles and the Law of Sines

7-2 The Ambiguous Case of the Law of Sines

7-3 The Law of Cosines

7-4 Geometrically Defined Vectors and Applications

7-5 Algebraically Defined Vectors and the Dot Product

Test Prep

Review Exercises

Test

8. Complex Numbers, Polar Equations, and Parametric Equations

8-1 Complex Numbers

8-2 Trigonometric (Polar) Form of Complex Numbers

8-3 The Product and Quotient Theorems

8-4 De Moivre’s Theorem

8-5 Polar Equations and Graphs

8-6 Parametric Equations, Graphs, and Applications

Test Prep

Review Exercises

Test

Answers to Selected Exercises

Photo Credits

Index