The function can be described using Unit Step Functions, since the signal is turned on at t = 0 and turned off at t = π, as follows:

f(t) = sin t • [u(t) − u(t − π)]

Now for the Laplace Transform:

{sin t • [u(t) − u(t − π)]} = {sin t • u(t)} − {sin t • u(t − π)}

Now, we need to express the second term all in terms of (t − π).

From trigonometry, we have:

sin(t − π) = -sin t

So we can write:

{sin t • u(t)} − {sin t • u(t − π)}

= {sin t • u(t)} + {sin(t − π) • u(t − π)}