> You are teaching a group of skeptical high school students trigonometry and > they need to know "Why do we learn Trigonometry?" > > 1. The trig functions are indissoluably connected with "normal" functions such as 1/(x^2+1), sqrt(1 - x^2). The connections will be made when they study calculus. In order to understand the connections, students should first of all understand the functions.
2. The sine and cosine are among the building blocks of applied mathematics (I'm thinking of Fourier series, Laplace transforms, etc.)
3. Polar coordinates, and complex numbers use trigonometric representations, so the sine and cosine are among the building blocks of mathematics itself.
On the other hand, resolving trig identities often receives too much attention. (Did you ever read W. Churchill's autobiography where he describes finally hitting a familiar identity on the Sandhurst entrance exam?).
Similarly, there is too much attention paid to the cotangent and cosecant. They really are not used. Personally, I would scrap the secant, too, but my colleagues feel differently.
M. J. Winter
Professor M. J. Winter email with attachments: Department of Mathematics or when network is busy: Michigan State University email@example.com East Lansing, MI 48824 fax: 517.432.1562 http://math.msu.edu/~winter/ telephone: 517.353.6337