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The hyperbolic functions represent an expansion of trigonometry beyond the circular functions. Both types depend on an argument , either circular angle or hyperbolic angle . Since the area of a circular sector with radius r and angle u (in radians) is r 2 u /2 , it will be equal to u when r = √ 2 .
These identities are useful whenever expressions involving trigonometric functions need to be simplified. An important application is the integration of non-trigonometric functions: a common technique involves first using the substitution rule with a trigonometric function , and then simplifying the resulting integral with a trigonometric identity.
The following is a list of integrals (anti-derivative functions) of hyperbolic functions. For a complete list of integral functions, see list of integrals. In all formulas the constant a is assumed to be nonzero, and C denotes the constant of integration.
Pages in category "Hyperbolic functions" The following 25 pages are in this category, out of 25 total. This list may not reflect recent changes. ...
For each inverse hyperbolic integration formula below there is a corresponding formula in the list of integrals of inverse trigonometric functions. The ISO 80000-2 standard uses the prefix "ar-" rather than "arc-" for the inverse hyperbolic functions; we do that here.
In mathematics, hyperbolic trigonometry can mean: The study of hyperbolic triangles in hyperbolic geometry (traditional trigonometry is the study of triangles in plane geometry) The use of the hyperbolic functions; The use of gyrotrigonometry in hyperbolic geometry
2.3 Trigonometric, inverse trigonometric, hyperbolic, and inverse hyperbolic functions relationship 2.4 Modified-factorial denominators 2.5 Binomial coefficients
List of integrals of hyperbolic functions; I. ... List of integrals of trigonometric functions This page was last edited on 19 November 2019, at 17:59 (UTC). ...
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