## Definitions

### from The American Heritage® Dictionary of the English Language, 5th Edition.

- 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. - noun The hyperbolic sine, defined by the equation sinh
*x*=^{1}/_{2}(*e*−^{x}*e*^{−}).^{x} - noun The hyperbolic cosine, defined by the equation cosh
*x*=^{1}/_{2}(*e*+^{x}*e*^{−}).^{x} - noun The hyperbolic tangent, defined by the equation tanh
*x*= sinh*x*/cosh*x.* - noun The hyperbolic cotangent, defined by the equation coth
*x*= cosh*x*/sinh*x.* - noun The hyperbolic secant, defined by the equation sech
*x*= 1/cosh*x.* - noun The hyperbolic cosecant, defined by the equation csch
*x*= 1/sinh*x.*

### from Wiktionary, Creative Commons Attribution/Share-Alike License.

- noun
*mathematics*Afunction that is derived from some arithmetic operations on theexponential function with basee and theinverse function , and was named after the corresponding similartrigonometric function .

## Etymologies

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## Examples

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