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The [[inverse hyperbolic functions]] are:
* '''areainverse hyperbolic sine''' "{{math|arsinh}}" (also denoted "{{math|sinh<sup>−1</sup>}}", "{{math|asinh}}" or sometimes "{{math|arcsinh}}")<ref>{{Citation | last=Woodhouse | first = N. M. J. | author-link = N. M. J. Woodhouse | title = Special Relativity | publisher = Springer | place = London | date = 2003 | page = 71 | isbn = 978-1-85233-426-0}}</ref><ref>{{Citation | editor1-last=Abramowitz | editor1-first=Milton | editor1-link=Milton Abramowitz | editor2-last=Stegun | editor2-first=Irene A. | editor2-link=Irene Stegun | title=Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables | publisher=[[Dover Publications]] | ___location=New York | isbn=978-0-486-61272-0 | year=1972| title-link=Abramowitz and Stegun }}</ref><ref>[https://www.google.com/books?q=arcsinh+-library Some examples of using '''arcsinh'''] found in [[Google Books]].</ref>
* '''areainverse hyperbolic cosine''' "{{math|arcosh}}" (also denoted "{{math|cosh<sup>−1</sup>}}", "{{math|acosh}}" or sometimes "{{math|arccosh}}")
* '''areainverse hyperbolic tangent''' "{{math|artanh}}" (also denoted "{{math|tanh<sup>−1</sup>}}", "{{math|atanh}}" or sometimes "{{math|arctanh}}")
* '''areainverse hyperbolic cotangent''' "{{math|arcoth}}" (also denoted "{{math|coth<sup>−1</sup>}}", "{{math|acoth}}" or sometimes "{{math|arccoth}}")
* '''areainverse hyperbolic secant''' "{{math|arsech}}" (also denoted "{{math|sech<sup>−1</sup>}}", "{{math|asech}}" or sometimes "{{math|arcsech}}")
* '''areainverse hyperbolic cosecant''' "{{math|arcsch}}" (also denoted "{{math|arcosech}}", "{{math|csch<sup>−1</sup>}}", "{{math|cosech<sup>−1</sup>}}","{{math|acsch}}", "{{math|acosech}}", or sometimes "{{math|arccsch}}" or "{{math|arccosech}}")
[[File:Hyperbolic functions-2.svg|thumb|upright=1.4|A [[Ray (geometry)|ray]] through the [[unit hyperbola]] {{math|1=''x''<sup>2</sup> − ''y''<sup>2</sup> = 1}} at the point {{math|(cosh ''a'', sinh ''a'')}}, where {{mvar|a}} is twice the area between the ray, the hyperbola, and the {{mvar|x}}-axis. For points on the hyperbola below the {{mvar|x}}-axis, the area is considered negative (see [[:Image:HyperbolicAnimation.gif|animated version]] with comparison with the trigonometric (circular) functions).]]
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