Table of Contents

• About these Study Guides
• This Guide and Mathematics Competitions
• On Competition Names
• On Competition Success
• This Guide and the Craft of Solving Problems
• This Guide and Mathematics Content: Trigonometry
• For Educators: This Guide and the Common Core State Standards
• Part I: Trigonometry
• 1. The Backbone Theorem: The Pythagorean Theorem
• 2. Some Surprisingly Helpful Background History
• 3. The Basics of "Circle-ometry"
• 4. Radian Measure
• 5. The Graphs of Sine and Cosine in Degrees
• 6. The Graphs of Sine and Cosine in Radians
• 7. Basic Trigonometric Identities
• 8. Sine and Cosine for Circles of Different Radii
• 9. A Paradigm Shift
• 10. The Basics of Trigonometry
• 11. The Tangent, Cotangent, Secant, and Cosecant Graphs
• 12. Inverse Trigonometric Functions
• 13. Addition and Subtraction Formulas; Double and Half Angle Formulas
• 14. The Law of Cosines
• 15. The Area of a Triangle
• 16. The Law of Sines
• 17. Heron's Formula for the Area of a Triangle
• 18. Fitting Trigonometric Functions to Periodic Data
• 19. (EXTRA) Polar Coordinates
• 20. (EXTRA) Polar Graphs
• Part II: Solutions
• Solutions
• Appendix: Ten Problem-Solving Strategies

Reviews

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