Question

How do you get the Laplace transform of: sin(t+pi) ??

Answer 1

It might be useful that \( \sin (t + \pi) = - \sin t \). This comes from logic of the unit circle, moving \( \pi\) units around the unit circle starts you off where sin becomes more negative.

Answer 2

With that, Laplace transform is just linear, so if you know the Laplace transform of \( \sin t \) you just tack on the negative sign.
\( \mathcal{L} \left( - \sin t \right) = - \mathcal{L} \left( \sin t \right) \)

Answer 3

I honestly don't remember that identity, and I can't find it on the list I tore out from my trig book. But that would make it easy...

Answer 4

If you know the angle sum identity on the trig sheet, that should also work:
\( \sin \left( t + \pi \right) = \sin t \cancel{ \cos \pi} \ -1 + \cancel{\sin \pi \cos t} \ 0 \)

Answer 5

Ok I see that now thank you

Answer 6

Glad to help. :)