The author might call this a short course on trigonometry but I think it would make a great refresher course or supplementary text for students. It was written by David E. Joyce, Professor of Mathematics and Computer Science at Clark University.
Students attempting this course should be familiar with algebra and geometry.
Table of Contents
- 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
View this Free Online Material at the source:
Dave’s Short Course on Trigonometry
