# Math Help - Laplacian Inverse Calculation

1. ## Laplacian Inverse Calculation

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

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

-Dan

3. Yep, just didn't see it because I'm retarded. Thanks.

4. 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