You are here

Trigonometry: A Clever Study Guide

James Tanton
MAA Press
Publication Date: 
Number of Pages: 
Problem Book Series
[Reviewed by
Mark Bollman
, on

The MAA has been publishing problem books for many years. It has also been the force behind American Mathematics Competitions. So it’s natural that they would publish problem books based on AMC problems. This is the first of a series of books collating AMC problems on specific themes.

There is a lot to like in the notion of books devoted to competitive mathematics, and the idea of collecting AMC problems thematically shows great promise of developing into a good resource for students preparing for contest mathematics and for those who coach them. While the series will draw largely on the AMC’s contests, the material in this book, and potentially others in the series, will certainly find use at all competitive levels.

Those of us who are involved with the world of mathematics competitions — at any level, high school or college — know that many good contest problems can be solved with a careful use of results from trigonometry. 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.

If this book is any indicator, these books will be an excellent addition to the MAA Problem Books series.

Mark Bollman ( is professor of mathematics and chair of the department of mathematics and computer science at Albion College in Michigan. His mathematical interests include number theory, probability, and geometry. Mark’s claim to be the only Project NExT fellow (Forest dot, 2002) who has taught both English composition and organic chemistry to college students has not, to his knowledge, been successfully contradicted. If it ever is, he is sure that his experience teaching introductory geology will break the deadlock.

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 1: 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
Appendix: Ten Problem-Solving Strategies