Arcsine in LaTeX (\arcsin)

Where it is used

Arcsine, the inverse of sine restricted to [-pi/2, pi/2], as an upright operator.

\arcsin x returns the angle in [-\pi/2, \pi/2] whose sine is x, for x in [-1, 1]. It is the unambiguous alternative to \sin^{-1} x, which some readers misread as 1/\sin x. Its derivative \frac{1}{\sqrt{1-x^2}} gives the standard integral \int \frac{dx}{\sqrt{1-x^2}} = \arcsin x + C, a staple of trigonometric substitution. Software libraries call it asin, but programming names should not appear in typeset math; always use the backslashed command so it prints upright and spaced. Group compound arguments with parentheses.

Minimal compilable example

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

\documentclass{article}
\begin{document}
Arcsine: $\arcsin$

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

Related symbols

• Arccosine\arccos
• Cosecant\csc
• Arctangent\arctan
• Secant\sec
• Arccotangent\text{arccot}
• Cotangent\cot

Frequently asked questions

How do I write Arcsine in LaTeX?

Type \arcsin in math mode, for example $\int \frac{dx}{\sqrt{1 - x^2}} = \arcsin x + C$. It works in plain LaTeX without loading any package.

Which package do I need for \arcsin?

None. \arcsin is part of standard LaTeX, so it compiles with nothing in the preamble but the document class.

Can I use \arcsin in text mode, or only in math mode?

Only in math mode. Outside $...$ LaTeX stops with "Missing $ inserted", so write $\arcsin$ in running text.