# Trigonometry: A Clever Study Guide

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*James Tanton*

MAA Press: An Imprint of the American Mathematical Society

This guide covers the story of trigonometry. It is a swift overview, but it is complete in the context of the content discussed in beginning and advanced high-school courses. The purpose of these notes is to supplement and put into perspective the material of any course on the subject you may have taken or are currently taking. (These notes will be tough going for those encountering trigonometry for the very first time!)

#### Reviews & Endorsements

The real unique feature of this book is the set of ten problem solving strategies that Tanton employs when he solved the featured problems. … Tanton references these strategies in his descriptions of solving the featured problems and manages to inject a bit of humor into the work. Trigonometry is a topic that is core to the understanding of basic mathematics and in this book Tanton emphasizes that even experienced mathematicians will look at problems and have an initial reaction of “What?” If you teach trig, there are many interesting and effective pedagogical techniques in this book as well as problems that you can use.

-- Charles Ashbacher

This clearly written, engaging book combines a summary of high school trigonometry and a guide to problem solving. The book offers teachers ideas about how to present some topics in an interesting way along with a collection of challenging problems involving trigonometry. … If you are looking for an excellent collection of challenging problems that use trigonometry or for a well-written review of trigonometry, this book would be a good choice.

-- Mathematics Teacher

… This book collects the most meaningful results from trigonometry and, in addition to reviewing them for the reader, includes a robust collection of problems from previous contests, where their value to competitors can be easily demonstrated. While this is not a textbook, a nice added feature is the connections to Common Core state standards. It's good to see that contest mathematics need not be separate from day-to-day classroom mathematics, and that there's more to contest uses of trigonometry than just clever tricks. …

-- Mark Bollman, MAA Reviews

# Table of Contents

## Trigonometry: A Clever Study Guide

- Cover cov11
- Half title i2
- Copyright ii3
- Title iii4
- Series iv5
- Contents vii8
- About these Study Guides ix10
- This Guide and Mathematics Competitions xi12
- This Guide and the Craft of Solving Problems xiii14
- This Guide and Mathematics Content: Trigonometry xv16
- For Educators:This Guide and the Common Core State Standards xvii18
- Part I: Trigonometry 122
- 1. The Backbone Theorem: The Pythagorean Theorem 324
- 2. Some Surprisingly Helpful Background History 1334
- 3. The Basics of "Circle-ometry'' 1839
- 4. Radian Measure 2950
- 5. The Graphs of Sine and Cosine in Degrees 3455
- 6. The Graphs of Sine and Cosine in Radians 3960
- 7. Basic Trigonometric Identities 4465
- 8. Sine and Cosine for Circles of Different Radii 4970
- 9. A Paradigm Shift 5374
- 10. The Basics of Trigonometry 5677
- 11. The Tangent, Cotangent, Secant, and Cosecant Graphs 7394
- 12. Inverse Trigonometric Functions 7697
- 13. Addition and Subtraction Formulas; Double and Half Angle Formulas 89110
- 14. The Law of Cosines 107128
- 15. The Area of a Triangle 116137
- 16. The Law of Sines 119140
- 17. Heron's Formula for the Area of a Triangle 125146
- 18. Fitting Trigonometric Functions to Periodic Data 133154
- 19. (EXTRA) Polar Coordinates 141162
- 20. (EXTRA) Polar Graphs 145166

- Part II: Solutions 149170