# Hyperbolic functions

Introduction to hyperbolic functions and learn hyperbolic functions from basics to advanced level.

A function that expressed in terms of exponential form functions is called a hyperbolic function.

## List of functions

Hyperbolic functions are six types and here is the list of six hyperbolic functions in exponential functions form for beginners.

01
##### Hyperbolic Sine Function

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

02
##### Hyperbolic Cosine Function

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

03
##### Hyperbolic Tangent Function

$\tanh{x} \,=\, \dfrac{e^x-e^{-x}}{e^x+e^{-x}}$

04
##### Hyperbolic Cotangent Function

$\coth{x} \,=\, \dfrac{e^x+e^{-x}}{e^x-e^{-x}}$

05
##### Hyperbolic Secant Function

${\mathop{\rm sech}\nolimits}^{-1}{x} \,=\, \dfrac{2}{e^x+e^{-x}}$

06
##### Hyperbolic Cosecant Function

${\mathop{\rm csch}\nolimits}^{-1}{x} \,=\, \dfrac{2}{e^x-e^{-x}}$

### Inverse Hyperbolic functions

The six hyperbolic functions also have inverse functions. Learn the mathematical form of inverse hyperbolic functions with proofs in mathematics.