Definition:Inverse Cotangent/Terminology
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Terminology for Inverse Cotangent
There exists the popular but misleading notation $\cot^{-1} x$, which is supposed to denote the inverse cotangent function.
However, note that as $\cot x$ is not an injection, it does not have a well-defined inverse.
The $\arccot$ 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 $\cot^{-1} x$, which (as pointed out) can be confusing and misleading.
Sometimes, $\operatorname {Cot}^{-1}$ (with a capital $\text C$) is taken to mean the same as $\arccot$.
However this can also be confusing due to the visual similarity between that and the lowercase $\text c$.
Some sources hyphenate: arc-cotangent.