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1. Who should take this course?
• Trigonometry for you
• Your background
• 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. Angle measurement
• The concept of angle
• Radians and arc length
• Exercises, hints, and answers
5. Chords
• What is a chord?
• Trigonometry began with chords
6. Sines
• The relation between sines and chords
• Sines and right triangles
• Exercises, hints, and answers
7. 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
8. Tangents and slope
• The definition of the tangent
• Tangent in terms of sine and cosine
• Tangents and right triangles
• Slopes of lines
• Common angles again
• Exercises, hints, and answers
9. 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
10. The trigonometric functions and their inverses (writing now)
11. The trigonometry of oblique triangles
• Solving oblique triangles
• The law of cosines
• The law of sines
• Exercises, hints, and answers
12. Summary of trigonometric identities
• More important identities
• Less important identities
• Truly obscure identities
13. Polar coordinates (yet to write)

Note: If your browser is Java-enabled, you can drag the points around in the diagrams and the diagram will adjust itself. The free points, colored red, can be freely dragged about, and as they move, the rest of the diagram (except the other free points) will adjust appropriately. Sliding points, colored orange, can be dragged about like the free points, except their motion is limited to either a straight line or a circle, depending on the point. If you drag the pivot point, colored green, the entire diagram will be translated along with it. Other points can be dragged, too, if there is a pivot point showing, and the diagram will be rotated and dilated around the pivot point. Also, if you type r or the space key while the cursor is over the diagram, then the diagram will be reset to its original configuration. If you type u or return the figure will be lifted off the page into a separate window. Typing d or return while the cursor is over the window will return the diagram to the page. Note that you can resize the floating window to make the diagram larger.

Started July, 1996. Copyright © 1996, 1997.

David E. Joyce
Department of Mathematics and Computer Science
Clark University Worcester, MA 01610

Email: djoyce@clarku.edu

These files are located at http://aleph0.clarku.edu/~djoyce/java/trig