I never internalized why the set of functions $f_n(x) = \sin(nx)$ is not equicontinuous
I know I can show that it is not equicontinuous by definition, by choice of appropriate $x,y$ for $|x-y|<\delta$. But I do not quite understand this by examining the graph of $\sin(nx)$.
I also cannot say whether $\sin(nx)$ is or isn't equicontinuous immediately just by looking at the function $\sin(nx)$.
Can someone who is knowledgable on this topic demonstrate how exactly you can tell from the graph of a set of functions whether such set is or is not equicontinuous?