hyperbolic function

hyperbolic function

noun

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 = ¹₂( e^x − e ⁻ ^x ).

b. The hyperbolic cosine, defined by the equation cosh x = ¹₂( e^x + 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.

THE AMERICAN HERITAGE® DICTIONARY OF THE ENGLISH LANGUAGE, FIFTH EDITION by the Editors of the American Heritage Dictionaries. Copyright © 2016, 2011 by Houghton Mifflin Harcourt Publishing Company. Published by Houghton Mifflin Harcourt Publishing Company. All rights reserved.

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"hyperbolic function." YourDictionary, n.d. Web. 09 December 2018. <https://www.yourdictionary.com/hyperbolic-function>.

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hyperbolic function. (n.d.). Retrieved December 09th, 2018, from https://www.yourdictionary.com/hyperbolic-function

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:

The hyperbolic sine, defined by the equation sinh x = ¹/₂(e^x − e^-x).
The hyperbolic cosine, defined by the equation cosh x = ¹/₂(e^x + e^-x).
The hyperbolic tangent, defined by the equation tanh x = sinh x/cosh x.
The hyperbolic cotangent, defined by the equation coth x = cosh x/sinh x.
The hyperbolic secant, defined by the equation sech x = 1/cosh x.
The hyperbolic cosecant, defined by the equation csch x = 1/sinh x.

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MLA Style

"hyperbolic function." YourDictionary, n.d. Web. 09 December 2018. <https://www.yourdictionary.com/hyperbolic-function>.

APA Style

hyperbolic function. (n.d.). Retrieved December 09th, 2018, from https://www.yourdictionary.com/hyperbolic-function

Noun

(plural hyperbolic functions)

(mathematics) A function that is derived from some arithmetic operations on the exponential function with base e and the inverse function, and was named after the corresponding similar trigonometric function.

English Wiktionary. Available under CC-BY-SA license.

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MLA Style

"hyperbolic function." YourDictionary, n.d. Web. 09 December 2018. <https://www.yourdictionary.com/hyperbolic-function>.

APA Style

hyperbolic function. (n.d.). Retrieved December 09th, 2018, from https://www.yourdictionary.com/hyperbolic-function

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