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# hyperbolic function

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.
[1885-90]

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In mathematics, one of a set of functions related to the hyperbola in the same way the trigonometric functions relate to the circle.

They are the hyperbolic sine, cosine, tangent, secant, cotangent, and cosecant (written "sinh," "cosh," etc.). The hyperbolic equivalent of the fundamental trigonometric identity is cosh2z -sinh2z = 1. The hyperbolic sine and cosine, particularly useful for finding special types of integrals, can be defined in terms of exponential functions: sinhx = (ex -e-x) ÷ 2 and coshx = (ex + e-x) ÷ 2

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Universalium. 2010.

### Look at other dictionaries:

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• hyperbolic function — noun Date: circa 1890 any of a set of six functions analogous to the trigonometric functions but related to the hyperbola in a way similar to that in which the trigonometric functions are related to a circle …   New Collegiate Dictionary

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