Application of the Uniform limit theorem

Calculus Level 2

For $n\in \mathbb{N}$ , let $f_n:[0, \pi]\to \mathbb{R}$ be defined by

$f_n(x):= \sin^n (x)$

Is the sequence $\{f_n\}_{n=1}^{\infty}$ uniformly convergent?

Hint: is the limit function continuous?

This problem is often posed in calculus textbooks.