# Math Help - Cosine Transform Question

1. ## Cosine Transform Question

Hi,

I'm trying to solve:

$f(t) = cos(\omega t) : 0 < t < T$

And I've got as far as this:

$\frac{1}{\omega}(\frac{\omega T}{2}+\frac{sin2 \omega T}{4})$

$\frac{\omega T}{2 \omega}+\frac{1}{4 \omega}sin2 \omega T$

$\frac{T}{2}+\frac{1}{4 \omega}sin2 \omega T$

However I don't understand how to algebraically solve this for the given answer:

$\frac{T}{2}(1+\frac{sin2 \omega T}{2 \omega T})$

I don't see how the right term has obtained the denominator $T$ underneath $sin2 \omega T$

I'm wondering if my tutor has made a mistake?

Any help would be appreciated.
Thanks in advance.

2. ## Re: Cosine Transform Question

You don't make it clear what it is that you are trying to do. You say solve, but solve what I don't know, only guess. Do they not have equals signs in Kent ?
As to the bit at the end though, you should be able to see that if you multiply out the bracket you'll get the line above.

3. ## Re: Cosine Transform Question

Ah.. got it now, was having a slow moment.

Many thanks.