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Full Description
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!)
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
