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## Book Description

- Follows a standard course curriculum.

- Includes both polar coordinates and complex numbers, unlike the competition.

## Table of Contents

1. Cover
2. Title Page
3. Dedication
4. Copyright
5. Contents
6. Introduction
7. Part 1: The Basic Tools
1. 1 What Is Trigonometry?
2. 2 Geometry Tools Needed to Study Trigonometry
1. Right Triangles
2. More on Triangles
3. Circles, Arcs, and Chords
3. 3 Algebra Tools Needed to Study Trigonometry
1. Cartesian Coordinates
2. What Are Functions?
3. Complex Numbers
8. Part 2: Triangle Trigonometry
1. 4 Trigonometric Functions and Right Triangles
1. The Tangent Ratio
2. Introducing the Sine and Cosine Ratios
3. Practical Applications of Trigonometric Ratios
4. Practice Problems
2. 5 Relations Among Trigonometric Ratios
1. Six Trigonometric Relatives
2. Determining Values of Trigonometric Functions
3. Solving Right Triangles
4. Practice Problems
3. 6 The Law of Sines
1. Oblique Triangles
2. The Sine of an Obtuse Angle
3. The Ambiguous Case
4. Solving Oblique Triangles Using the Law of Sines
5. Practice Problems
4. 7 The Law of Cosines
1. The Law of Cosines
2. Two Cases That the Law of Cosines Helps to Solve
3. Application of Trigonometry to Navigation and Surveying
4. Hero’s Formula for the Area of a Triangle
5. Practice Problems
9. Part 3: Trigonometric Functions and the Unit Circle
1. 8 Angles and Rotations
1. Measuring Angles
2. Sectors of Circles
3. Practice Problems
2. 9 The Unit Circle Approach
1. What Is the Unit Circle?
2. Placing Points on the Unit Circle
3. Making Sense of the Unit Circle
4. Evaluating Trigonometric Functions of Real Numbers
5. Practice Problems
3. 10 Trigonometric Functions of Any Angle
1. Calculating Values of Trigonometric Functions
2. Reference Angles
3. Evaluating Trigonometric Functions
4. Looking Closely at Trigonometric Functions
5. Practice Problems
10. Part 4: Graphs of Trigonometric Functions
1. 11 Graphs of Sine and Cosine Functions
1. Basic Sine Curve
2. Other Sinusoidal Curves
3. Translations of the Sine Curve
4. The Cosine Curve
5. Modeling Periodic Behavior
6. Practice Problems
2. 12 Graphs of Other Trigonometric Functions
1. Graphs of Tangent Function
2. Graphs of Cotangent Function
3. Graphs of the Reciprocal Functions
4. Graphing Combinations of Functions
5. Practice Problems
3. 13 Graphs of Inverse Trigonometric Functions
1. Inverse Sine Function
2. Other Inverse Trigonometric Functions
1. Inverse Cosine and Tangent Functions
2. Inverses of Reciprocal Trigonometric Functions
3. Sample Problem 2
4. Sample Problem 3
5. Compositions of Trig and Inverse Trig Functions
6. Practice Problems
11. Part 5: Trigonometric Identities and Equations
1. 14 Kaleidoscope of Identities
1. Basic Identities
2. Many Uses of the Fundamental Identities
3. Practice Problems
2. 15 Verifying Trigonometric Identities
1. Important Guidelines
2. Different Tactics for Verifying Identities
3. Practice Problems
3. 16 Solving Trigonometric Equations
1. What It Means to Solve a Trigonometric Equation
2. Solving Techniques
3. Equations of Quadratic Type
4. When Multiple Angles Are Involved
5. Practice Problems
4. 17 Sum and Difference Formulas
1. Sum and Difference Formulas for Sine and Cosine
2. Applying Formulas to Various Trig Problems
3. Practice Problems
5. 18 Double-Angle and Power-Reducing Formulas
1. Double-Angle Formulas
2. Power-Reducing Formulas
3. Practice Problems
6. 19 Half-Angle and Product-to-Sum Formulas
1. Half-Angle Formulas
2. Product–to-Sum Formulas
3. Sum-to-Product Formulas
4. How to Avoid Frustration While Working with Formulas
5. Practice Problems
12. Part 6: Polar Coordinates and Complex Numbers
1. 20 Polar Coordinates
1. Introducing Polar Coordinates
2. Coordinate Conversions
3. Converting Polar Equations to Rectangular Form
4. Graphs of Polar Equations
5. Practice Problems
2. 21 Complex Numbers and Operations with Them
1. Geometric Representation of Complex Numbers
2. Converting from One Form to Another
3. Product of Two Complex Numbers in Polar Form
4. De Moivre’s Theorem and Powers of Complex Numbers
5. Roots of Complex Numbers
6. Practice Problems
3. 22 Trigonometry and Calculators?
1. Calculators That Can Help You with Trigonometry
2. Evaluating Trigonometric Functions
3. Evaluating Inverse Trigonometric Functions
4. Sketching Graphs of Trigonometric Functions
5. Solving Trig Equations with a Calculator
13. Appendixes
14. Index