Definition:Inverse Sine/Complex/Definition 1

Definition
Let $z \in \C$ be a complex number.

The inverse sine of $z$ is the multifunction defined as:
 * $\sin^{-1} \paren z := \set {w \in \C: \sin \paren w = z}$

where $\sin \paren w$ is the sine of $w$.

Also see

 * Equivalence of Definitions of Complex Inverse Sine Function


 * Definition:Complex Arcsine