# Definition:Cosecant/Analysis

## Definition

#### Real Function

Let $x \in \C$ be a real number.

The real function $\csc x$ is defined as:

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

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

The definition is valid for all $x \in \R$ such that $\sin x \ne 0$.

#### Complex Function

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 $\sin z \ne 0$.