some of a collection of six features related, for a proper or complex adjustable x, on hyperbola in a way analogous on relationship of this trigonometric functions to a circle, including:

The hyperbolic sine, defined because of the equation sinh x = 1/2 (ex - e-x).

The hyperbolic cosine, defined because of the equation cosh x = 1/2 (ex + e-x).

The hyperbolic tangent, defined because of the equation tanh x = sinh x/cosh x.

The hyperbolic cotangent, defined by the equation coth x = cosh x/sinh x.

The hyperbolic secant, defined by the equation sech x = 1/cosh x.

The hyperbolic cosecant, defined by the equation csch x = 1/sinh x.

A function this is certainly produced from some arithmetic functions from the exponential purpose with base age additionally the inverse purpose, and had been called following the corresponding comparable trigonometric purpose.

## How would you define hyperbolic function?