Stiletto One

OK, so I can get sine transforms. How do I do a cosine transform?!

also...
sin at = [e^(ait) - e^(-ait)]/2i
cos at = [e^(ait) + e^(-ait)]/2i
...right? I can get the transform for cosine to look right, except I'm left with a (1/i) coefficient dangling in the equation.

Cramming for an exam, figured I'd post this in a place with a high geek concentration.

Anglican

L(sin t) is Im(L(e^it)) whilst L(cos t) is the real part, you should be able to figure out the rest from there.

nermal

I might be interpereting your question wrong, but the Laplace Transform for a Cosine function Cos(at) is:

s
__________
s^2 + a^2

Are you asking something else? I had to go back to the books for this. I even needed a refresher on IBP. :banghead:

Ed

Anglican

I think he knows what the transform is, he just wants to know how it's derived.

nermal

Ah. Now I look and see he's using Euler. I missed that the first time around.
I just integrated the thing and grunted it out. Silly me.

Ed

harsh

Um, your Euler formula for Cos is incorrect. Cosine does not have an (i) in the denominator. I think that should solve your problem.

Stiletto One

DAMMIT :banghead:

Thanks, that's what I thought.

harsh

No problem. Good luck on the exam.