# Laplace Transform of squared trig functions help?

1. Oct 1, 2012

### chief10

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..

SOLVED

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.

-chief10

Last edited: Oct 1, 2012
2. Oct 1, 2012

### Mute

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.

3. Oct 1, 2012

### chief10

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.