# Laplacian Inverse Calculation

• Apr 3rd 2011, 08:32 AM
ragnar
Laplacian Inverse Calculation
So I'm to find $\displaystyle \mathcal{L}^{-1}\{e^{-\pi}}/(s^{2}+1)\}$ and I figure it should just be: The exponential tells me its unit step-functioned over by $\displaystyle \pi$ and then just Laplacian inverse the leftover so the result is $\displaystyle \sin(t-\pi) \mathcal{U}(t-\pi)$. My book says it's $\displaystyle -\sin t \mathcal{U}(t-\pi)$ and I don't get it.
• Apr 3rd 2011, 08:36 AM
topsquark
Quote:

Originally Posted by ragnar
So I'm to find $\displaystyle \mathcal{L}^{-1}\{e^{-\pi}}/(s^{2}+1)\}$ and I figure it should just be: The exponential tells me its unit step-functioned over by $\displaystyle \pi$ and then just Laplacian inverse the leftover so the result is $\displaystyle \sin(t-\pi) \mathcal{U}(t-\pi)$. My book says it's $\displaystyle -\sin t \mathcal{U}(t-\pi)$ and I don't get it.

Isn't sin(t - Pi) = -sin(t)?

-Dan
• Apr 3rd 2011, 08:38 AM
ragnar
Yep, just didn't see it because I'm retarded. Thanks.
• Apr 3rd 2011, 08:41 AM
topsquark
Quote:

Originally Posted by ragnar
Yep, just didn't see it because I'm retarded. Thanks.

Don't beat yourself up. We've all been there. :)

-Dan