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 — A ray through the origin intercepts the hyperbola in the point , where is twice the area between the ray and the …   Wikipedia

  • hyperbolic function — noun 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. See Also: hyperbolic sine, hyperbolic cosine,… …   Wiktionary

  • hyperbolic function — hy′perbol′ic func′tion n. math. 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 • Etymology: 1885–90 …   From formal English to slang

  • 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

  • hyperbolic function — /haɪpəˌbɒlɪk ˈfʌŋkʃən/ (say huypuh.bolik fungkshuhn) noun one of the six mathematical functions which express angles in terms of distances between points on a hyperbola; analogous to the trigonometrical ratios, they are written sinh, cosh, tanh,… …   Australian English dictionary

  • inverse hyperbolic function — noun The inverse of a hyperbolic function Syn: antihyperbolic function, arc hyperbolic function …   Wiktionary

  • arc-hyperbolic function — noun An inverse hyperbolic function …   Wiktionary

  • Inverse hyperbolic function — The inverses of the hyperbolic functions are the area hyperbolic functions. The names hint at the fact that they compute the area of a sector of the unit hyperbola x^{2} y^{2} = 1 in the same way that the inverse trigonometric functions compute… …   Wikipedia

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