# Dave’s Short Trig Course

1. Who should take this course?
• Trigonometry for you
• How to learn trigonometry

2. Applications of trigonometry
• Astronomy and geography
• Engineering and physics
• Mathematics and its applications

3. What is trigonometry?
• Trigonometry as computational geometry
• Angle measurement and tables

4. Background on geometry
• The Pythagorean theorem
• An explanation of the Pythagorean theorem
• Similar triangles

5. Angle measurement
• The concept of angle

6. Chords
• What is a chord?
• Trigonometry began with chords

7. Sines
• The relation between sines and chords
• The word “sine”
• Sines and right triangles
• The standard notation for a right triangle

8. Cosines
• Definition of cosine
• Right triangles and cosines
• The Pythagorean identity for sines and cosines
• Sines and cosines for special common angles

9. Tangents and slope
• The definition of the tangent
• Tangent in terms of sine and cosine
• Tangents and right triangles
• Slopes of lines
• Angles of elevation and depression
• Common angles again

10. The trigonometry of right triangles
• Solving right triangles
• Inverse trig functions: arcsine, arccosine, and arctangent
• The other three trigonometric functions: cotangent, secant, and cosecant
• Pythagorean triples

11. The trigonometric functions and their inverses
• Arbitrary angles and the unit circle
• Sines and cosines of arbitrary angles
• Properties of sines and cosines that follow from the definition
• Graphs of sine and cosine functions
• Graphs of tangent and cotangent functions
• Graphs of secant and cosecant functions

12. Computing trigonometric functions
• Before computers: tables
• After computers: power series

13. The trigonometry of oblique triangles
• Solving oblique triangles
• The law of cosines
• The law of sines

14. Demonstrations of the laws of sines and cosines
• For the law of sines
• For the law of cosines

15. Area of a triangle
• Area in terms of two sides and the included angle

16. Ptolemy’s sum and difference formulas
• Ptolemy’s theorem
• The sum formula for sines
• The other sum and difference formulas

17. Summary of trigonometric formulas
• Formulas for arcs and sectors of circles
• Formulas for right triangles
• Formulas for oblique triangles
• Formulas for areas of triangles

18. Summary of trigonometric identities
• More important identities
• Less important identities
• Truly obscure identities

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