hyperbolic function

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.

hyperbolic function

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 )

hyperbolic function

/ 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.

Word History and Origins

Origin of hyperbolic function¹

First recorded in 1885–90