# hyperbolic function

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Related to Arcsinh: Arccosh, Arcsech, Arctanh

## 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 ?
In this case the field is given by [phi] = [+ or -] i arcsinh [[square root of ([gamma]r)] / [square root of ([gamma])] and the potential reads V([phi]) [equivalent] -6[gamma].
plana over day after treatment (DAT) [+ or -] s.e 11 DAT 30 DAT Methamidophos 0.0 [+ or -] 0.0 [+ or -] (Product 1) 0.0 a (100%) 0.0 a (100%) Methamidophos 0.0 [+ or -] 0.0 [+ or -] (Product 2) 0.0 a (100%) 0.0 a (100%) Monocrotophos 2.1 0.9 [+ or -] 0.0 [+ or -] (Product 1) 0.0 a (98.52%) 0.0 a (100%) Monocrotophos 1.0 [+ or -] 0.00 [+ or -] (Product 2) 0.9 a (99.33%) 0.0 a (100%) Monocrotophos 0.8 [+ or -] 0.0 [+ or -] (Product 3) 0.4 a (99.49%) 0.0 a (100%) Untreated 415.0 [+ or -] 50.3 [+ or -] 11.5 b (+210.46%) 3.8 b (62.30%) F value 48.5 3862.6 P Value 0.00 0.00 Means in columns with same letters are not significantly different (P>0.05) by Tukey's test after arcsinh transformation DAT = Days after treatment Numbers in bracket are % of reduction of M.
I prefer to use the ArcSinH function (Stretch / ArcSinH), which provides excellent control of the light and dark areas of the image.
X = A arcsinh S/A, Y = F + A -[square root of ([A.sup.2] + [S.sup.2])], (24)

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