# Hyperbolic Function

Hyperbolic functions are similar to trigonometric functions. These functions are denoted by sinh, cosh, tanh, cosech (csch), sech, coth and are pronounced as hyperbolic sin (or sin hyperbolic), hyperbolic cos, hyperbolic tan, hyperbolic cosec, hyperbolic sec, hyperbolic cot. Unlike trigonometric functions which are defined in context with right triangle, hyperbolic functions are defined as exponential expressions.

Sine and cosine are defined as follows:

- $\sinh x$ = $\frac{e^{x}-e^{-x}}{2}$
- $\cosh x$ = $\frac{e^{x}+e^{-x}}{2}$

Expressions of all other hyperbolic functions can be derived by using above two relations.