Question

How can I do this?\[\mathcal{L}\left \{ \delta(t-\pi)\cos(t) \right \}\]

Answer 1

I know that\[\mathcal{L}\left \{ \cos(t)\right \}=\frac{s}{s^2+1}\]and\[\mathcal{L}\left \{ \delta(t-\pi)\right \}=e^{-\pi s}.\]But I have no idea how to proceed.

Answer 2

Judging from the answer to this question (back of the book), can I assume that\[\mathcal{L}\left \{ \delta(t-a)f(t) \right \}=e^{-as}f(a)?\]

Answer 3

It says\[\mathcal{L}\left \{ \delta(t-\pi)\cos(t) \right \}=-e^{-\pi s}\]and\[\mathcal{L}\left \{ \delta(t-\pi)\sin(t) \right \}=0.\]