Taylor Series Homework: Find Series for f(x)=sin x at a=pi/2

[rcmango]

Homework Statement

Find the Taylor series for f(x) = sin x centered at a = pi / 2

Homework Equations

The Attempt at a Solution

Taylor series is a new series for me.

I believe the first step is to start taking the derivative of the Taylor series.

f(x) = sinx
f'(x) = cosx
f''(x) = -sinx
f'''(x) = -cosx
f(4)x= sinx
...
f(n)x = sin(x)^n

now do i start plugging in the a = pi/2 for x?
Okay, not sure what I'm trying to prove with a taylor series, and why to use it, what's next.

Also, I have to prove that the series converges to sinx on (-infinity, infinity)

Thanks.

 

[NateTG]

http://en.wikipedia.org/wiki/Taylor_series
http://mathworld.wolfram.com/TaylorSeries.html