trigonometry - Solving limits of a sine wave $lim_{xto+infty}frac{sin(x)}{x}$

So I got this assignment. And I was wondering how is it possible to get a limit from a constantly changing formula.
$$\lim_{x\to+\infty}\frac{\sin(x)}{x}$$
Can I only look in the domain $]0,2\pi[$?

Answer

A possible approach is to take help of the following:

1. $$\lim_{x\to+\infty}\frac{1}{x}=0$$




2. $$-1\le\sin x\le1$$