How do I find the horizontal asymptote of $f(x)=\frac{\sin (x) }{x}$? I can instantly see that there will be a vertical asymptote at $x=0$, however I am finding it quite a challenge to find a horizontal asymptote. I've drawn the graph and it seems as if the amplitude of this function decreases as we tend towards infinity, however that is the only remarkable thing I can say about it. Can someone help point out where I am going wrong. Thank you.
There is no vertical asymptote at $x = 0$. As for horizontal asymptotes,

$$\left| \frac{\sin x}{x} \right| \leq \left|\frac{1}{x}\right| \ \rightarrow 0 \ \hbox{ as } x \rightarrow \pm\infty$$
https://www.khanacademy.org/math/ap-calculus-ab/ab-derivative-rules/ab-derivtive-rules-opt-vids/v/sinx-over-x-as-x-approaches-0
This link shows the proof that why when limit approaches 0,sinx/x equals to 1.