# hyperbolic function

(redirected from Osborne's rule)
Related to Osborne's rule: Hyperbolic trigonometric functions

## hyperbolic function

n.
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:
a. The hyperbolic sine, defined by the equation sinh x = 1/2 (ex - e-x).
b. The hyperbolic cosine, defined by the equation cosh x = 1/2 (ex + e-x).
c. The hyperbolic tangent, defined by the equation tanh x = sinh x/cosh x.
d. The hyperbolic cotangent, defined by the equation coth x = cosh x/sinh x.
e. The hyperbolic secant, defined by the equation sech x = 1/cosh x.
f. The hyperbolic cosecant, defined by the equation csch x = 1/sinh x.

## hyperbolic function

n
(Mathematics) 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)

## hy′perbol′ic func′tion

n.
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.
[1885–90]
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References in periodicals archive ?
It's feared Osborne's rules, which are set to come into force in October, can only be enforced by an army of inspectors armed with thermometers patrolling our streets.
Jamie Osborne's Rules For Jokers (9-2), carrying the colours of Timeform's Jim McGrath and Reg Griffin, gained a remarkable victory in the Maraval Nursery having been drawn worst of all in stall 18.

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