1. ## Equicontinuous

Prove or disprove
$F_n(x) = \sin nx$ is equicontinuous

I know the definition of equicontinuous at $x_0$ it says for all $\epsilon >0$ there exist $\delta>0$ such that if $d ( f(x_0),f(x) ) < \epsilon$ then
$d(x_0 , x) < \delta$

trying if it is equicontinuous at $x_0 = 0$
Given $\epsilon > 0$

$| f(x) | < \epsilon \Rightarrow |\sin n x | < \epsilon$
delta depends on epsilon and x just how i can continue

any hints or any directions

2. ## Re: Equicontinuous

Do we have to decide whether the family is equi-continuous at each point, or to determine the point on which the family is equi-continuous? For the first question, look at $F_n\left(\frac{\pi}{2n}\right)$.