# Convolve returns false result

Bug introduced in 9.0 or earlier and fixed in 10.0

I tried to convolve sin with sin and got this unexpected result:

Convolve[Sin[x], Sin[x], x, y]
(* 0 *)


Now I know convolution of infinite functions is not well defined, but normalized for the length of the interval, the solution should look like $-\frac{\cos(y)}{2}$. Ignoring that, the answer should at least be $\infty$, or undefined, but definitely not zero.