# Package or command for inverse hyperbolic trig functions?

What are the commands for all the:

• inverse trig functions (arcsec(x), arcCsc(x), arcCot(x));
• hyperbolic trig functions (sech(x) and csch(x)), and
• inverse hyperbolic trig functions?
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@Ian - thank you for the appropriate tags (this now comes up as the top hit on google when you search the functions + latex)! –  Rax Adaam Feb 8 at 13:07

After spending some time looking for this, I found this post that suggested defining the new commands for the omitted inverse trig functions.

Here I've augmented that with the full suit of hyperbolic and inverse hyperbolic functions for convenience, as google doesn't turn anything up for this search, nor does the other post come up if one is searching for the inverse hyperbolic functions, specifically.

\documentclass{article}

\usepackage{amsmath}
\DeclareMathOperator{\sech}{sech}
\DeclareMathOperator{\csch}{csch}
\DeclareMathOperator{\arcsec}{arcsec}
\DeclareMathOperator{\arccot}{arcCot}
\DeclareMathOperator{\arccsc}{arcCsc}
\DeclareMathOperator{\arccosh}{arcCosh}
\DeclareMathOperator{\arcsinh}{arcsinh}
\DeclareMathOperator{\arctanh}{arctanh}
\DeclareMathOperator{\arcsech}{arcsech}
\DeclareMathOperator{\arccsch}{arcCsch}
\DeclareMathOperator{\arccoth}{arcCoth}

\begin{document}
$\sech x \cschx \arcsec x \arccot x \arccsc x \arccosh x \arcsinh x \arctanh x \arcsech x arccsch x \arccoth x$
\end{document}

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@Christian Thank you for cleaning up the entry, how did you get the proper formatting? I spent an age trying to get it to display properly, but it wouldn't recognize line breaks, so I modified it to make it legible & left it at that. Thank you! –  Rax Adaam Feb 8 at 13:06
You just need to select the code and either click the {} button over the textfield or simply press ctrl+k. This will indent your code by 4 spaces, which then is recognized as code. –  xfoo Feb 8 at 13:15
These definitions are very practical! However, inverse hyperbolic functions don't have 'c' in the name: arsinh, arcosh, artgh... because they give the area of the hyperbolic sector, rather than arc of the triangle. We have trigonometric and hyperbolic functions and their respective inverses, such as "arcus sinus" and "area cosinus hyperbolicus", though pronunciation differs from original Latin. –  Vladimir Jun 14 at 2:58