hyperbolic function

(redirected from Hyperbolic curve)

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.
American Heritage® Dictionary of the English Language, Fifth Edition. Copyright © 2016 by Houghton Mifflin Harcourt Publishing Company. Published by Houghton Mifflin Harcourt Publishing Company. All rights reserved.

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)
Collins English Dictionary – Complete and Unabridged, 12th Edition 2014 © HarperCollins Publishers 1991, 1994, 1998, 2000, 2003, 2006, 2007, 2009, 2011, 2014

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]
Random House Kernerman Webster's College Dictionary, © 2010 K Dictionaries Ltd. Copyright 2005, 1997, 1991 by Random House, Inc. All rights reserved.
References in periodicals archive ?
Generally, intersection line between contour surface and voxel boundary surface is hyperbolic curve. When two branches of hyperbolic curve are intersected with some boundary surface, ambiguity of connection means comes up.
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We have to go up the hyperbolic curve and have people's candidates everywhere in the city from Bhayandar to Colaba," asserts Vora.
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The State-level interim estimates are based on: (a) data reported by the States (e.g., production data for Alaska are typically reported to the EIA before the interim estimate is made); (b) first purchase data reported on Form EIA-182, "Domestic Crude Oil First Purchase Report;" (c) exponential or hyperbolic curve fitted projections based on recent State data; or (d) constant level projections based on the average production rate during a recent time period.
How useful is a hyperbolic curve for quotients in these circumstances?
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However, by determining the difference between the times of arrival at two sites, we can know that the transmitting site is located along a hyperbolic curve. If the TDOA is measured very accurately, the emitter location will be very dose to the line, but since a hyperbola is an infinite curve, the location problem is not yet solved.