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Appendix B: The Unit Circle
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Appendix B: The Unit Circle
by W. Michael Kelley
The Humongous Book of Trigonometry Problems
Cover
Title Page
Copyright
Contents
Introduction
Acknowledgements
Trademarks
Dedication
Chapter 1: Angles and Arcs
Standard Position
Measuring Angles
Converting Between Angle Measurements
Complementary and Supplementary Angles
Arc Length
Chapter 2: Right Triangle Trigonometry
Pythagorean Theorem
Trigonometric Functions
Trigonometric Tables
Calculator-Generated Trigonometric Values
Chapter 3: The Unit Circle
45°–45°–90° Triangles
30°–60°–90° Triangles
Cosine and Sine in the First Quadrant
Common Angles on the Unit Circle
Chapter 4: Trigonometric Values of General Angles
Reference Angles
Coterminal Angles
Angles Beyond the Unit Circle
Chapter 5: Graphing Sine and Cosine Functions
Periodic Functions
Transforming Periodic Graphs
Sine Functions
Cosine Functions
Chapter 6: Graphing Other Trigonometric Functions
Tangent
Cotangent
Secant
Cosecant
Chapter 7: Basic Trigonometric Identities
Reciprocal and Cofunction Identities
Negative Identities
Pythagorean Identities
Sum and Difference Formulas for Sine and Cosine
Chapter 8: Advanced Trigonometric Identities
Double-Angle Formulas
Power-Reducing Formulas
Half-Angle Formulas
Product-to-Sum Identities
Sum-to-Product Identities
Tangent Identities
Chapter 9: Inverse Trigonometric Functions
Graphs of Inverse Trigonometric Functions
General and Exact Solutions
Chapter 10: Simple Trigonometric Equations
Linear Equations
Zero Products
Quadratic Formula
Functions of Multiple Angles
Chapter 11: Advanced Trigonometric Equations
Square Roots
Rational Equations
Pythagorean Identities
Squaring
Applying Trigonometric Identities
Chapter 12: Area of Triangles and Sectors
Base and Height
Trigonometric Area Formulas
Heron’s Formula
Area of a Sector
Chapter 13: Oblique Triangle Laws
Law of Sines
Law of Cosines
Chapter 14: Vectors
Plotting Vectors
Component Form
Magnitude
Unit Vectors
Chapter 15: Basic Vector Operations
Adding and Subtracting Graphically
Adding and Subtracting Algebraically
Scalar Multiplication
Identifying Components Given Magnitude and Direction
Chapter 16: Advanced Vector Operations
Dot Product
Measuring Angles Between Vectors
Orthogonal Vectors
Vector Projections and Work
Chapter 17: Parametric Equations and Polar Coordinates
Parametric Equations
Polar Coordinates
Converting Between Polar and Rectangular Form
Polar Graphs
Chapter 18: Trigonometry of Complex Numbers
Rectangular Form of Complex Numbers
Trigonometric Form of Complex Numbers
Multiplying and Dividing Trigonometric Form
De Moivre’s Theorem
Roots of Complex Numbers
Appendix A: Table of Trigonometric Values
Appendix B: The Unit Circle
Appendix C: Formulas and Identities
Index
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Appendix A: Table of Trigonometric Values
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Appendix C: Formulas and Identities
Appendix B
THE UNIT CIRCLE
Just in case you didn’t memorize it
ANGLES MEASURED IN RADIANS
ANGLES MEASURED IN DEGREES
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