# Definition:Real Hyperbolic Tangent/Definition 2

## Definition

The real hyperbolic tangent function is defined on the real numbers as:

$\tanh: \R \to \R$:
$\forall x \in \R: \tanh x := \dfrac {\sinh x} {\cosh x}$

where:

$\sinh$ is the real hyperbolic sine
$\cosh$ is the real hyperbolic cosine