Calculating tan to power -1

I have an equation of the form $$ a = \tan^{-1}\frac{y}{x} $$

is this the same as

$$ a = \frac{1}{\tan\,\left.y\middle/x\right.} $$

It has been over 20 years since doing math and I cannot find any answers on google.

1 Answer

There is some confusion in this area. Usually, for any integer power, it is common to write $\tan^n(x)$ instead of $(\tan(x))^n$. If this is the case, then $\tan^{-1}(x)=\frac{1}{\tan(x)}$

However, there is a very annoying habit in some part of the community in which the term $\tan^{-1}$ actually refers to the $\arctan$.

Personally, I find it very annoying when $\tan^{-1}$ is used to denote the inverse function instead of the power.