# Hyperbolic-function definition

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.*

noun

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*).^{&spminus;x} - The
**hyperbolic cosine,**defined by the equation cosh*x*=^{1}/_{2}(*e*+^{x}*e*).^{&spminus;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.*

## Other Word Forms

### Noun

Singular:

hyperbolic-function
Plural:

hyperbolic functions