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Math Help - Cosine Transform Question

  1. #1
    Junior Member
    Joined
    Apr 2010
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    Kent, U.K
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    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.
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  2. #2
    Super Member
    Joined
    Jun 2009
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    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.
    Thanks from ashleysmithd
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  3. #3
    Junior Member
    Joined
    Apr 2010
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    Kent, U.K
    Posts
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    Re: Cosine Transform Question

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

    Many thanks.
    Last edited by ashleysmithd; June 10th 2012 at 08:42 AM.
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