## hyperbolic function

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:a. The hyperbolic sine, defined by the equation sinh

*x*=^{1}/_{2}(*e*−^{x}*e*^{−}*).*^{x}b. The hyperbolic cosine, defined by the equation cosh

*x*=^{1}/_{2}(*e*+^{x}*e*^{−}*).*^{x}c. The hyperbolic tangent, defined by the equation tanh

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

*x*= cosh*x*/sinh*x.*e. The hyperbolic secant, defined by the equation sech

*x*= 1/cosh*x.*f. The hyperbolic cosecant, defined by the equation csch

*x*= 1/sinh*x.*## hyperbolic function

Noun

(*plural* hyperbolic functions)

- (mathematics) A function that is derived from some arithmetic operations on the exponential function with base e and the inverse function, and was named after the corresponding similar trigonometric function.

- hyperbolic sine
- hyperbolic cosine
- hyperbolic tangent