# Definition:Inverse Cotangent/Terminology

Jump to navigation
Jump to search

## 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.**