Give the Laplace transform of the expression! > Given the equation $u_π(t)sin(at)$, where $u_τ(t)$ is the Heaviside step function. > Give the Laplace transform $Y(s)$. In order to use the formula $L\\{u_c(t)\cdot f(t-c)\\}=e^{-cs}\cdot F(s)$ I have to rewrite $sin(at)$, my idea was to write it as $-sin(at-\pi)$ but is not enough because I need inside the $sine$ $(t-\pi)$ and not $(at-\pi)$, how can I rewrite it in order to use the above formula? Thanks in advance! :)

Hint: another variant of the transform law is

$$\mathcal{L}\\{u_c(t)f(t)\\}=e^{-cs}F(s+c)$$

which lets you do a shift after the transform instead of before. This way, you only need the transform of $\sin(at)$, rather than the function shifted.