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== History ==
The first known calculation of a hyperbolic trigonometry problem is attributed to [[Gerardus Mercator]] when issuing the [[Mercator projection|Mercator map projection]] circa 1566. It requires tabulating solutions to a transcendental equation involving hyperbolic functions.<ref>{{Cite book |last=George F. Becker |url=https://archive.org/details/hyperbolicfuncti027682mbp/page/n49/mode/2up?q=mercator |title=Hyperbolic Functions |last2=C. E. Van Orstrand |date=1909 |publisher=The Smithsonian Institution |others=Universal Digital Library}}</ref>
The first to suggest a similarity between the sector of the circle and that of the hyperbola was [[Isaac Newton]] in his 1687 [[Philosophiæ Naturalis Principia Mathematica|''Principia Mathematica'']].<ref name=":0">{{Cite book |last=McMahon |first=James |url=https://archive.org/details/hyperbolicfuncti031883mbp/page/n75/mode/2up |title=Hyperbolic Functions |date=1896 |publisher=John Wiley And Sons |others=Osmania University, Digital Library Of India}}</ref>
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Hyperbolic functions were introduced in the 1760s independently by [[Vincenzo Riccati]] and [[Johann Heinrich Lambert]].<ref>Bradley, Robert E.; D'Antonio, Lawrence A.; Sandifer, Charles Edward. ''Euler at 300: an appreciation.'' Mathematical Association of America, 2007. Page 100.</ref> Riccati used {{math|''Sc.''}} and {{math|''Cc.''}} ({{lang|la|sinus/cosinus circulare}}) to refer to circular functions and {{math|''Sh.''}} and {{math|''Ch.''}} ({{lang|la|sinus/cosinus hyperbolico}}) to refer to hyperbolic functions. Lambert adopted the names, but altered the abbreviations to those used today.<ref>Becker, Georg F. ''Hyperbolic functions.'' Read Books, 1931. Page xlviii.</ref> The abbreviations {{math|sh}}, {{math|ch}}, {{math|th}}, {{math|cth}} are also currently used, depending on personal preference.
[[François Daviet de Foncenex|Daviet de Foncenex]] showed the interchangeability of the trigonometric and hyperbolic functions using the imaginary unit and extended [[de Moivre's formula]] to hyperbolic functions.<ref name=":0" />
== Notation ==
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