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The Humongous Book of Trigonometry Problems

Book Description

Most math and science study guides are a reflection of the college professors who write them-dry, difficult, and pretentious.

The Humongous Book of Trigonometry Problems is the exception. Author Mike Kelley has taken what appears to be a typical trigonometry workbook, chock full of solved problems-more than 750!-and made notes in the margins adding missing steps and simplifying concepts and solutions, so what would be baffling to students is made perfectly clear. No longer will befuddled students wonder where a particular answer came from or have to rely on trial and error to solve problems. And by learning how to interpret and solve problems as they are presented in a standard trigonometry course, students become fully prepared to solve those difficult, obscure problems that were never discussed in class but always seem to find their way onto exams.

Table of Contents

  1. Cover
  2. Title Page
  3. Copyright
  4. Contents
  5. Introduction
  6. Acknowledgements
  7. Trademarks
  8. Dedication
  9. Chapter 1: Angles and Arcs
    1. Standard Position
    2. Measuring Angles
    3. Converting Between Angle Measurements
    4. Complementary and Supplementary Angles
    5. Arc Length
  10. Chapter 2: Right Triangle Trigonometry
    1. Pythagorean Theorem
    2. Trigonometric Functions
    3. Trigonometric Tables
    4. Calculator-Generated Trigonometric Values
  11. Chapter 3: The Unit Circle
    1. 45°–45°–90° Triangles
    2. 30°–60°–90° Triangles
    3. Cosine and Sine in the First Quadrant
    4. Common Angles on the Unit Circle
  12. Chapter 4: Trigonometric Values of General Angles
    1. Reference Angles
    2. Coterminal Angles
    3. Angles Beyond the Unit Circle
  13. Chapter 5: Graphing Sine and Cosine Functions
    1. Periodic Functions
    2. Transforming Periodic Graphs
    3. Sine Functions
    4. Cosine Functions
  14. Chapter 6: Graphing Other Trigonometric Functions
    1. Tangent
    2. Cotangent
    3. Secant
    4. Cosecant
  15. Chapter 7: Basic Trigonometric Identities
    1. Reciprocal and Cofunction Identities
    2. Negative Identities
    3. Pythagorean Identities
    4. Sum and Difference Formulas for Sine and Cosine
  16. Chapter 8: Advanced Trigonometric Identities
    1. Double-Angle Formulas
    2. Power-Reducing Formulas
    3. Half-Angle Formulas
    4. Product-to-Sum Identities
    5. Sum-to-Product Identities
    6. Tangent Identities
  17. Chapter 9: Inverse Trigonometric Functions
    1. Graphs of Inverse Trigonometric Functions
    2. General and Exact Solutions
  18. Chapter 10: Simple Trigonometric Equations
    1. Linear Equations
    2. Zero Products
    3. Quadratic Formula
    4. Functions of Multiple Angles
  19. Chapter 11: Advanced Trigonometric Equations
    1. Square Roots
    2. Rational Equations
    3. Pythagorean Identities
    4. Squaring
    5. Applying Trigonometric Identities
  20. Chapter 12: Area of Triangles and Sectors
    1. Base and Height
    2. Trigonometric Area Formulas
    3. Heron’s Formula
    4. Area of a Sector
  21. Chapter 13: Oblique Triangle Laws
    1. Law of Sines
    2. Law of Cosines
  22. Chapter 14: Vectors
    1. Plotting Vectors
    2. Component Form
    3. Magnitude
    4. Unit Vectors
  23. Chapter 15: Basic Vector Operations
    1. Adding and Subtracting Graphically
    2. Adding and Subtracting Algebraically
    3. Scalar Multiplication
    4. Identifying Components Given Magnitude and Direction
  24. Chapter 16: Advanced Vector Operations
    1. Dot Product
    2. Measuring Angles Between Vectors
    3. Orthogonal Vectors
    4. Vector Projections and Work
  25. Chapter 17: Parametric Equations and Polar Coordinates
    1. Parametric Equations
    2. Polar Coordinates
    3. Converting Between Polar and Rectangular Form
    4. Polar Graphs
  26. Chapter 18: Trigonometry of Complex Numbers
    1. Rectangular Form of Complex Numbers
    2. Trigonometric Form of Complex Numbers
    3. Multiplying and Dividing Trigonometric Form
    4. De Moivre’s Theorem
    5. Roots of Complex Numbers
  27. Appendix A: Table of Trigonometric Values
  28. Appendix B: The Unit Circle
  29. Appendix C: Formulas and Identities
  30. Index