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Topic: Why trig?
Replies: 21   Last Post: Apr 3, 1997 4:17 PM

 Messages: [ Previous | Next ]
 M.J.Winter Posts: 24 Registered: 12/3/04
Re: Why trig?
Posted: Mar 31, 1997 1:17 PM

> 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 winter@tcimet.net
East Lansing, MI 48824 fax: 517.432.1562
http://math.msu.edu/~winter/ telephone: 517.353.6337