# Definition:Inverse Cosecant/Terminology

## Terminology for Inverse Cosecant

There exists the popular but misleading notation $\csc^{-1} x$, which is supposed to denote the inverse cosecant function.

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

The $\arccsc$ 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 $\csc^{-1} x$, which (as pointed out) can be confusing and misleading.

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

However this can also be confusing due to the visual similarity between that and the lowercase $\text {c}$.

Some sources hyphenate: arc-cosecant.