hyperbolic function

American  

noun

Mathematics.

1. 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.

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hyperbolic function British  

noun

1. any of a group of functions of an angle expressed as a relationship between the distances of a point on a hyperbola to the origin and to the coordinate axes. The group includes sinh ( hyperbolic sine ), cosh ( hyperbolic cosine ), tanh ( hyperbolic tangent ), sech ( hyperbolic secant ), cosech ( hyperbolic cosecant ), and coth ( hyperbolic cotangent )

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hyperbolic function Scientific  

/ hī′pər-bŏl′ĭk /

1. 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:

   1. The hyperbolic sine, defined by the equation sinh x = 1/2 (e ^x − e ^{- x}).

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

   3. The hyperbolic tangent, defined by the equation tanh x = sinh x /cosh x.

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

   5. The hyperbolic secant, defined by the equation sech x = 1/cosh x.

   6. The hyperbolic cosecant, defined by the equation csch x = 1/sinh x.

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Etymology

Origin of hyperbolic function

First recorded in 1885–90