The period of $\sin(nx)$

Question

How can I prove with induction that period of $\sin(nx)$ is $\frac{2\pi}{n}$? I know how to prove this using a different method, but I need to prove it with induction.

Answer 1

Note that $$f(x)$$ hase nthe period $T$ if $$f(x+T)=f(x)$$ for all $$x$$ in the domain of $$f(x)$$