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eBook ISBN:  9781614444060 
Product Code:  PRB/25.E 
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AMS Member Price:  $37.50 
Softcover ISBN:  9780883858363 
eBook: ISBN:  9781614444060 
Product Code:  PRB/25.B 
List Price:  $115.00 $90.00 
MAA Member Price:  $86.25 $67.50 
AMS Member Price:  $86.25 $67.50 
Softcover ISBN:  9780883858363 
Product Code:  PRB/25 
List Price:  $65.00 
MAA Member Price:  $48.75 
AMS Member Price:  $48.75 
eBook ISBN:  9781614444060 
Product Code:  PRB/25.E 
List Price:  $50.00 
MAA Member Price:  $37.50 
AMS Member Price:  $37.50 
Softcover ISBN:  9780883858363 
eBook ISBN:  9781614444060 
Product Code:  PRB/25.B 
List Price:  $115.00 $90.00 
MAA Member Price:  $86.25 $67.50 
AMS Member Price:  $86.25 $67.50 

Book DetailsProblem BooksVolume: 25; 2015; 211 pp
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 highschool 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!)

Table of Contents

Chapters

Part I. Trigonometry

Chapter 1. The Backbone Theorem: The Pythagorean Theorem

Chapter 2. Some Surprisingly Helpful Background History

Chapter 3. The Basics of “Circleometry”

Chapter 4. Radon Measure

Chapter 5. The Graphs of Sine and Cosine in Degrees

Chapter 6. The Graphs of Sine and Cosine in Radians

Chapter 7. Basic Trigonometric Identities

Chapter 8. Sine and Cosine for Circles of Different Radii

Chapter 9. A Paradigm Shift

Chapter 10. The Basics of Trigonometry

Chapter 11. The Tangent, Cotangent, Secant, and Cosecant Graphs

Chapter 12. Inverse Trigonometric Functions

Chapter 13. Addition and Subtraction Formulas; Double and Half Angle Formulas

Chapter 14. The Law of Cosines

Chapter 15. The Area of a Triangle

Chapter 16. The Law of Sines

Chapter 17. Herron’s Formula for the Area of a Triangle

Chapter 18. Fitting Trigonometric Functions to Periodic Data

Chapter 19. (EXTRA) Polar Coordinates

Chapter 20. (EXTRA) Polar Graphs

Part II. Solutions

Solutions

Appendix: Ten ProblemSolving Strategies


Additional Material

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 wellwritten 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 daytoday classroom mathematics, and that there's more to contest uses of trigonometry than just clever tricks. ...
Mark Bollman, MAA Reviews


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 Book Details
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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 highschool 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!)

Chapters

Part I. Trigonometry

Chapter 1. The Backbone Theorem: The Pythagorean Theorem

Chapter 2. Some Surprisingly Helpful Background History

Chapter 3. The Basics of “Circleometry”

Chapter 4. Radon Measure

Chapter 5. The Graphs of Sine and Cosine in Degrees

Chapter 6. The Graphs of Sine and Cosine in Radians

Chapter 7. Basic Trigonometric Identities

Chapter 8. Sine and Cosine for Circles of Different Radii

Chapter 9. A Paradigm Shift

Chapter 10. The Basics of Trigonometry

Chapter 11. The Tangent, Cotangent, Secant, and Cosecant Graphs

Chapter 12. Inverse Trigonometric Functions

Chapter 13. Addition and Subtraction Formulas; Double and Half Angle Formulas

Chapter 14. The Law of Cosines

Chapter 15. The Area of a Triangle

Chapter 16. The Law of Sines

Chapter 17. Herron’s Formula for the Area of a Triangle

Chapter 18. Fitting Trigonometric Functions to Periodic Data

Chapter 19. (EXTRA) Polar Coordinates

Chapter 20. (EXTRA) Polar Graphs

Part II. Solutions

Solutions

Appendix: Ten ProblemSolving Strategies

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 wellwritten 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 daytoday classroom mathematics, and that there's more to contest uses of trigonometry than just clever tricks. ...
Mark Bollman, MAA Reviews