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# hyperbolic function

## noun

,

*Mathematics.*- a function of an angle expressed as a relationship between the distances from a point on a hyperbola to the origin and to the coordinate axes, as hyperbolic sine or hyperbolic cosine: often expressed as combinations of exponential functions.

hyperbolic function

## noun

- any of a group of functions of an angle expressed as a relationship between the distances of a point on a hyperbola to the origin and to the coordinate axes. The group includes sinh (
**hyperbolic sine**), cosh (**hyperbolic cosine**), tanh (**hyperbolic tangent**), sech (**hyperbolic secant**), cosech (**hyperbolic cosecant**), and coth (**hyperbolic cotangent**)

hyperbolic function

/ hī′pər-bŏl**′**ĭk /

- Any of a set of six functions related, for a real or complex variable
*x,*to the hyperbola in a manner analogous to the relationship of the trigonometric functions to a circle, including:- The
**hyperbolic sine,**defined by the equation sinh*x*= 1 2 (*e*−^{x}*e*).^{-x} - The
**hyperbolic cosine,**defined by the equation cosh*x*= 1 2 (*e*+^{x}*e*).^{-x} - The
**hyperbolic tangent,**defined by 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.*

## Discover More

## Word History and Origins

Origin of hyperbolic function^{1}

First recorded in 1885–90

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