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Hyperbolic functions occur in the calculations of angles and distances in [[hyperbolic geometry]]. They also occur in the solutions of many linear [[differential equation]]s (such as the equation defining a [[catenary]]), [[Cubic equation#Hyperbolic solution for one real root|cubic equations]], and [[Laplace's equation]] in [[Cartesian coordinates]]. [[Laplace's equation]]s are important in many areas of [[physics]], including [[electromagnetic theory]], [[heat transfer]], [[fluid dynamics]], and [[special relativity]].
The basic hyperbolic functions are:<ref name=":1">{{Cite web|last=Weisstein|first=Eric W.|authorlink=Eric W. Weisstein|title=Hyperbolic Functions| url=https://mathworld.wolfram.com/HyperbolicFunctions.html|access-date=2020-08-29|website=mathworld.wolfram.com|language=en}}</ref>
* '''hyperbolic sine''' "{{math|sinh}}" ({{IPAc-en|ˈ|s|ɪ|ŋ|,_|ˈ|s|ɪ|n|tʃ|,_|ˈ|ʃ|aɪ|n}}),<ref>(1999) ''Collins Concise Dictionary'', 4th edition, HarperCollins, Glasgow, {{ISBN|0 00 472257 4}}, p. 1386</ref>
* '''hyperbolic cosine''' "{{math|cosh}}" ({{IPAc-en|ˈ|k|ɒ|ʃ|,_|ˈ|k|oʊ|ʃ}}),<ref name="Collins Concise Dictionary p. 328">''Collins Concise Dictionary'', p. 328</ref>
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