# Hyperbolic sine function

## Formula

$\large \sinh{x} \,=\, \dfrac{e^{\displaystyle x}-e^{\displaystyle -x}}{2}$

### Introduction

The ratio of the subtraction of neper constant $e$ raised to the power of negative real number from $e$ raised to the power of positive real number to the number $2$ is called the hyperbolic sine function.

The term hyperbolic sine is written as $\sinh$ in mathematics as its short form. If $x$ is a literal number and used to represent a real number, then the hyperbolic sine function is written as $\sinh{x}$.

#### Function

The definition of the hyperbolic sine function is expressed in mathematical form as follows.

$\sinh{x} \,=\, \dfrac{e^x-e^{-x}}{2}$

Save (or) Share