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Laplace Transform of squared trig functions help?

  1. Oct 1, 2012 #1
    now say we have cos^2(3t), how would you go about computing it with the 3t?

    i can manage cos^2(t) but i'm not sure how to take it that one step further

    in the link below is what i've managed so far..


    I worked it out.

    If anyone's interested in the future, Just start it off as cos^2(t). Solve it all the way through using the identity (1/2)(cos2t+1) <------- this identity can be split up and solved using your standard Laplace identities.

    Then identify the 3t from cos^2(3t). Realize that it's 3*ANGLE so multiply your integers in your final laplace transform of cos^2(t) by 3^2=9.

    Your two integers should end up as 18 in the numerator and 36 in your denominator.

    Hope this helps.

    Last edited: Oct 1, 2012
  2. jcsd
  3. Oct 1, 2012 #2


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    Homework Helper

    You could always use the identity

    $$\cos x = \frac{e^{ix}+e^{-ix}}{2},$$
    for x = 3t, and expand the square to get four purely exponential terms (of complex argument) which you can Laplace transform.
  4. Oct 1, 2012 #3
    so set the power of the exp as 3it?

    how would it look if you had four exp terms though? i'm having trouble conceptualizing that.
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