Definition:Inverse Tangent/Terminology

Terminology for Inverse Tangent
There exists the popular but misleading notation $\tan^{-1} x$, which is supposed to denote the inverse tangent function.

However, note that as $\tan x$ is not an injection, it does not have a well-defined inverse.

The $\arctan$ function as defined here has a well-specified image which (to a certain extent) is arbitrarily chosen for convenience.

Therefore it is preferred to the notation $\tan^{-1} x$, which (as pointed out) can be confusing and misleading.

Sometimes, $\operatorname {Tan}^{-1}$ (with a capital $\text T$) is taken to mean the same as $\arctan$.

In computer software packages, the notation $\operatorname {atan}$ or $\operatorname {atn}$ can sometimes be found.

Some sources hyphenate: arc-tangent.