# Definition:Inverse Secant/Terminology

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## Terminology for Inverse Secant

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

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

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

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

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

Some sources hyphenate: **arc-secant**.