Calculating the limit $ lim_{n to infty} frac{n}{4} cdot sin(4 pi/n) $.

I would like to calculate
$$\lim_{n\rightarrow \infty}\frac{n}{4} \sin \left(\frac{4 \pi}{n} \right)$$

Clearly this is a limit of the type $\infty \cdot 0$, so I'm thinking there is probably some way to turn it to $\infty / \infty$ or $0 / 0 $ and then use L'Hopital but I can't think of any such trick. I cannot think of a way to do it without L'Hoptial either. Thanks for any input.

Answer

HINT: If you can prove that
$$

\lim_{x\to 0}\frac{\sin x}{x}=1,
$$
then you are almost done by writing $x=4/n$ and letting $n\to \infty$.