# Definition:Cosecant/Complex Function

## Definition

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

The complex function $\csc z$ is defined as:

$\csc z = \dfrac 1 {\sin z}$

where $\sin z$ is the sine of $z$.

The definition is valid for all $z \in \C$ such that $\sin z \ne 0$.

## Also denoted as

The cosecant function:

$\csc$

can often be seen written as:

$\cosec$