Let $f_n(x)=\sin{(nx)}$. Show that $f_n\to 0$ in the distributional sense.
I know that this is true only if $\langle f_n,\phi\rangle=\int_{\mathbb{R}^n} f_n\phi\to \int_{\mathbb{R}^n} f\phi=\langle f,\phi\rangle$ for any test function $\phi$. In this case the 2nd integral equals $0$.
My question is how to go about implementing this. Any help would be welcome.