Laplace inverse of the sine function

Question

I was wondering if there is a closed-form Laplace inverse of the sine function. I have tried the following: $$ \sin(as)=\sum_{n=0}^{\infty}\frac{(-1)^{n}(as)^{2n+1}}{(2n+1)!} $$ an $n$-th power of $s$ contributes with an $n$-th derivative of the Dirac delta. So one expects a series expansion in terms of the Delta function and its derivatives. But that is utterly ugly! Hence the question.