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Hyperbolic functions take place in the answers of numerous linear differential equations (such as, the equation defining a catenary), of some cubic equations, in calculations of angles and distances in hyperbolic geometry, and of Laplace's equation in Cartesian coordinates.
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The spinoff of sinh x is cosh x as well as the derivative of cosh x is sinh x; this is analogous to trigonometric capabilities, albeit the signal is different (i.e., the derivative of cos x is −sin x).
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It may be proven that the world underneath the curve of cosh (x) more than a finite interval is usually equivalent into the arc duration equivalent to that interval:[twelve]
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