- Who should take this course?
- Trigonometry for you
- Your background
- How to learn trigonometry

- Applications of trigonometry
- Astronomy and geography
- Engineering and physics
- Mathematics and its applications

- What is trigonometry?
- Trigonometry as computational geometry
- Angle measurement and tables

- Background on geometry
- The Pythagorean theorem
- An explanation of the Pythagorean theorem
- Similar triangles

- Angle measurement
- The concept of angle
- Radians and arc length
- Exercises, hints, and answers
- About digits of accuracy

- Chords
- What is a chord?
- Trigonometry began with chords

- Sines
- The relation between sines and chords
- The word “sine”
- Sines and right triangles
- The standard notation for a right triangle
- Exercises, hints, and answers

- Cosines
- Definition of cosine
- Right triangles and cosines
- The Pythagorean identity for sines and cosines
- Sines and cosines for special common angles
- Exercises, hints, and answers

- 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
- Exercises, hints, and answers

- The trigonometry of right triangles
- Solving right triangles
- Inverse trig functions: arcsine, arccosine, and arctangent
- The other three trigonometric functions: cotangent, secant, and cosecant
- Exercises, hints, and answers
- Pythagorean triples

- 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

- Computing trigonometric functions
- Before computers: tables
- After computers: power series

- The trigonometry of oblique triangles
- Solving oblique triangles
- The law of cosines
- The law of sines
- Exercises, hints, and answers

- Demonstrations of the laws of sines and cosines
- For the law of sines
- For the law of cosines

- Area of a triangle
- Area in terms of two sides and the included angle

- Ptolemy’s sum and difference formulas
- Ptolemy’s theorem
- The sum formula for sines
- The other sum and difference formulas

- Summary of trigonometric formulas
- Formulas for arcs and sectors of circles
- Formulas for right triangles
- Formulas for oblique triangles
- Formulas for areas of triangles

- Summary of trigonometric identities
- More important identities
- Less important identities
- Truly obscure identities

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