Dave's Short Trig Course
Table of Contents
1. Who should take this course?
o Trigonometry for you
o Your background
o How to learn trigonometry
2. Applications of trigonometry
o Astronomy and geography
o Engineering and physics
o Mathematics and its applications
3. What is trigonometry?
o Trigonometry as computational geometry
o Angle measurement and tables
4. Background on geometry
o The Pythagorean theorem
o An explanation of the Pythagorean theorem
o Similar triangles
5. Angle measurement
o The concept of angle
o Radians and arc length
o Exercises, hints, and answers
o About digits of accuracy
6. Chords
o What is a chord?
o Trigonometry began with chords
7. Sines
o
o
o
o
o
The relation between sines and chords
The word "sine"
Sines and right triangles
The standard notation for a right triangle
Exercises, hints, and answers
8. Cosines
o Definition of cosine
o Right triangles and cosines
o The Pythagorean identity for sines and cosines
o Sines and cosines for special common angles
o Exercises, hints, and answers
9. Tangents and slope
o The definition of the tangent
o Tangent in terms of sine and cosine
o Tangents and right triangles
o Slopes of lines
o Angles of elevation and depression
o Common angles again
o Exercises, hints, and answers
10. The trigonometry of right triangles
o Solving right triangles
o Inverse trig functions: arcsine, arccosine, and arctangent
o The other three trigonometric functions: cotangent, secant, and cosecant
o Exercises, hints, and answers
o Pythagorean triples
11. The trigonometric functions and their inverses
o Arbitrary angles and the unit circle
o Sines and cosines of arbitrary angles
o Properties of sines and cosines that follow from the definition
o Graphs of sine and cosine functions
o Graphs of tangent and cotangent functions
o Graphs of secant and cosecant functions
12. Computing trigonometric functions
o Before computers: tables
o After computers: power series
13. The trigonometry of oblique triangles
o Solving oblique triangles
o The law of cosines
o The law of sines
o Exercises, hints, and answers
14. Demonstrations of the laws of sines and cosines
o For the law of sines
o For the law of cosines
15. Area of a triangle
o Area in terms of two sides and the included angle
16. Summary of trigonometric identities
o
o
o
More important identities
Less important identities
Truly obscure identities
About the Java applet.
Images in Dave's Short Trig Course are illustrated with a Java applet. If your browser is
Java-enabled, you can drag the points around in the diagrams and the diagram will adjust
itself. The applet also allows you to lift a diagram off the web page into its own floating
window. For details, see About the applet.
Note that most web browsers do not allow printers to print images created by Java
applets. If you want to print the images, turn off Java in your browser. Then the plain
images that appear can be printed.
Special symbols used here. Some old web browsers do not display mathematical
symbols. The following table shows the mathematical symbols used here. If there are any
entries in the first column that appear blank or appear as question marks, then your web
browser will not display those symbols, and you will need to use a different web browser
to see all the symbols.
Symbol
Select topic
Description
Example
–
minus sign
x–y
±
plus or minus sign
x±y
°
degree sign
45°
√
square root sign
√2
3
√
cube root sign
3
≠
not equal to
x≠y
≤
less than or equal to
x≤y
≥
greater than or equal to x ≥ y
√5
Started July, 1996. Copyright © 1996, 1997, 2002.
David E. Joyce
Department of Mathematics and Computer Science
Clark University Worcester, MA 01610
Dave's Short Trig Course is located at http://aleph0.clarku.edu/~djoyce/java/trig