My friend and I were discussing this and we couldn't figure out how to prove it one way or another.

The only rational values I can figure out for $\sin(x)$ (or $\cos(x)$, etc...) come about when $x$ is some product of a fraction of $\pi$.

Is $\sin(x) $ (or other trigonometric function) necessarily irrational if $ x $ is rational?

Edit: Excluding the trivial solution of 0.