Dave’s Short Course on Trigonometry

Written by: David E. Joyce (Clark University)

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
What is a chord?
Trigonometry began with chords
The relation between sines and chords
The word “sine”
Sines and right triangles
The standard notation for a right triangle
Exercises, hints, and answers
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

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