Contents

pp vii-viii

About these Study Guides

pp ix-x

This Guide and Mathematics Competitions

pp xi-xii

This Guide and the Craft of Solving Problems

pp xiii-xiv

This Guide and Mathematics Content: Trigonometry

pp xv-xvi

For Educators: This Guide and the Common Core State Standards

pp xvii-xx

Part I: Trigonometry

pp 1-2

1 - The Backbone Theorem: The Pythagorean Theorem

pp 3-12

2 - Some Surprisingly Helpful Background History

pp 13-17

3 - The Basics of “Circle-ometry”

pp 18-28

4 - Radian Measure

pp 29-33

5 - The Graphs of Sine and Cosine in Degrees

pp 34-38

6 - The Graphs of Sine and Cosine in Radians

pp 39-43

7 - Basic Trigonometric Identities

pp 44-48

8 - Sine and Cosine for Circles of Different Radii

pp 49-52

9 - A Paradigm Shift

pp 53-55

10 - The Basics of Trigonometry

pp 56-72

11 - The Tangent, Cotangent, Secant, and Cosecant Graphs

pp 73-75

12 - Inverse Trigonometric Functions

pp 76-88

13 - Addition and Subtraction Formulas; Double and Half Angle Formulas

pp 89-106

14 - The Law of Cosines

pp 107-115

15 - The Area of a Trian

pp 116-118

16 - The Law of Sines

pp 119-124

17 - Heron's Formula for the Area of a Triangle

pp 125-132

18 - Fitting Trigonometric Functions to Periodic Data

pp 133-140

19 - (EXTRA) Polar Coordinates

pp 141-144

20 - (EXTRA) Polar Graphs

pp 145-148

Part II: Solutions

pp 149-150

Solutions

pp 151-206