Definition:Inverse Sine/Terminology

Terminology for Inverse Sine

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

However, note that as $\sin x$ is not an injection (even though by restriction of the codomain it can be considered surjective), it does not have a well-defined inverse.

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

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

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

In computer software packages, the notation $\operatorname {asin}$ or $\operatorname {asn}$ can sometimes be found.

Some sources hyphenate: arc-sine.