How to find the derivative of trig functions?

[camila]

How would you find the derivative of sin(x), i know the answer but I don't know how you would derive the answer. I don't want it worked out the whole way but if you could just tell me the steps I need to take that would be great.
And are the other trig functions derived the same way?
Thanks!

[TI]

(1) You want to find the limit of the following expression (E) as h -->0:

E = [sin(x + h) - sin(x)]/h

(2) For this, expand sin(x + h) to obtain:

sin(x + h) = sin(x)cos(h) + cos(x)sin(h)

(3) Now, as h -->0, cos(h) -->1 and sin(h) -->h

so... as h --> 0

(4) E --> [sin(x) + h cos(x) - sin(x)]/h = h cos(x)/h = cos(x)

Hence, the derivative of sin(x) = cos(x)

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The derivatives of other basic trig functions can be derived

the same way.

[camila]

GOLD Thanks so much!!