Is the set $\{\frac{\sin nx}{n} : n = 1,2, \cdots\}$ equicontinuous on $\mathbb{R}$?

Question

Define a set of functions as $$ \tilde{f}=\{\frac{\sin nx}{n} : n = 1,2, \cdots\} $$ is $\tilde{f}$ equicontinuous on $\mathbb{R}$?

Answer 1

Since $\frac {\sin\, nx} {n} \to 0$ uniformly on $\mathbb R$ and each of these function is uniformly continuous it follows that the sequence is equicontinuous. [I will give a detailed proof if you are unable to use these hints].