TITLE: Why is $\cos(x)^2$ written as $\cos^2(x)$?
QUESTION [7 upvotes]: I'm just wondering why the square of $\cos(x)$ (i.e.: $(\cos(x))*(\cos(x))$) is almost universally written in the form $\cos^2(x)$ rather than $\cos(x)^2$.  This seems particularly bizarre when one considers that $\cos^{-1}(x) \ne \cos(x)^{-1}$.

REPLY [2 votes]: This is because composition of functions are very rare when you are talking about trigonometric functions.
For any other $f: \mathbb{D} \to \mathbb{R}$, it may make sense to calculate $f(f(x))$, however for $\sin(x)$ or $\cos(x)$, composition like $\cos(\cos(x))$ is not a frequent use. That's why a misunderstanding in $\cos^2(x)$ is not so much in concern.
On the other hand, when it is about $\arcsin(x)$ and $\csc(x)$, there are conflicts about the use of $\sin^{-1}(x)$.