Arcsecant in LaTeX (\text{arcsec})

Where it is used

Inverse secant, written with \text since LaTeX has no predefined \arcsec.

Defined for |x| \ge 1, \text{arcsec}\, x = \arccos(1/x). Its derivative is \frac{1}{|x|\sqrt{x^2-1}} under the usual range [0, \pi] excluding \pi/2, and the absolute value is a frequent omission in student work. Because \text adds no operator spacing, insert \, before the argument or switch to \operatorname{arcsec}. Declaring \DeclareMathOperator{\arcsec}{arcsec} once lets you write \arcsec x just like \arccos x. Integral tables express \int \frac{dx}{x\sqrt{x^2-1}} in terms of it. It is rarely used in modern papers, which tend to rewrite it as an arccosine of the reciprocal.

Minimal compilable example

Paste this into an empty .tex file and compile it with pdfLaTeX, XeLaTeX or LuaLaTeX.

\documentclass{article}
\usepackage{amsmath}
\begin{document}
Arcsecant: $\text{arcsec}$

\[ \int \frac{dx}{x\sqrt{x^2 - 1}} = \text{arcsec}\, x + C \]
\end{document}

Related symbols

• Arccosecant\text{arccsc}
• Arccotangent\text{arccot}
• Inverse Sine\sin^{-1}
• Arctangent\arctan
• Inverse Cosine\cos^{-1}
• Arccosine\arccos

Frequently asked questions

How do I write Arcsecant in LaTeX?

Type \text{arcsec} in math mode, for example $\int \frac{dx}{x\sqrt{x^2 - 1}} = \text{arcsec}\, x + C$. Load amsmath first with \usepackage{amsmath}.

Which package do I need for \text{arcsec}?

\text{arcsec} needs amsmath: add \usepackage{amsmath} to your preamble before the document starts.

Can I use \text{arcsec} in text mode, or only in math mode?

Both. \text{arcsec} compiles in running text as well as inside $...$; in a formula keep it in math mode so it gets math fonts and spacing.