Hyperbolic Function

Hyperbolic functions are analogues of the ordinary trigonometric functions, but defined using the hyperbola rather tan the circle. $cosh^{2} x - sinh^{2} x = 1$

We have the basic hyperbolic functions: $cosh x = \frac{e ^{x} + e ^{- x}}{2}$ $sinh x = \frac{e ^{x} - e ^{- x}}{2}$ $tanh x = \frac{e ^{x} - e ^{- x}}{e ^{x} + e ^{- x}}$