Definition:Cotangent/Analysis

Definition

Real Function

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

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

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

where:

• $\sin x$ is the sine of $x$
• $\cos x$ is the cosine of $x$
• $\tan x$ is the tangent 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 $\cot z$ 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 $\cos z \ne 0$.