Definition:Cotangent/Complex Function

Definition

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

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

$\cot z = \dfrac {\cos z} {\sin z} = \dfrac 1 {\tan z}$

where:

$\sin z$ is the sine of $z$
$\cos z$ is the cosine of $z$
$\tan z$ is the tangent of $z$

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