Let $\displaystyle h_n (x) = sin(nx)$. Is $\displaystyle h_n (x)$ uniformly convergent on the interval [0,1]?

I don't think that it is uniformly convergent but I'm having a hard time proving it. I thought to use the theorem that it will be uniformly convergent iff $\displaystyle \forall \epsilon >0 \exists N \in \mathbb{N} s.t. \forall n,m>N |f_n(x) - f_m(x)|\ <\epsilon$, but I can't see how to show this. Any help?