Definition:Inverse Tangent/Terminology
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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.