Prove that $\displaystyle f(x)=cos^3x$ is either uniform continuous or not.

I claim that this function is not, since its derivative is not bounded. But how do I show that using the definition?

Proof so far:

Let $\displaystyle \epsilon = 1 $, for every $\displaystyle \delta > 0 $, I need to find $\displaystyle x,y \in \mathbb {R} , |x-y| < \delta $ implies $\displaystyle |f(x)-f(y)| = |cos^3x - cos^3y| \geq 1 $

What kind of x and y should I pick?

Thanks.