Arccosine in LaTeX (\arccos)

Where it is used

Arccosine, returning the angle in [0, pi] whose cosine is a given value.

The angle between two vectors, \theta = \arccos\frac{\mathbf{a}\cdot\mathbf{b}}{\lVert\mathbf{a}\rVert\lVert\mathbf{b}\rVert}, is perhaps its most common appearance. Its range is [0, \pi] and its derivative is -\frac{1}{\sqrt{1-x^2}}, which is why \arcsin x + \arccos x = \frac{\pi}{2} for every x in [-1, 1]. \cos^{-1} x means the same thing, but \arccos avoids confusion with the reciprocal. Wrap long arguments in \left( \right) for clarity, since the operator supplies no brackets of its own. In computational geometry it is often clamped to [-1, 1] first to avoid rounding errors.

Minimal compilable example

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

\documentclass{article}
\begin{document}
Arccosine: $\arccos$

\[ \arcsin x + \arccos x = \frac{\pi}{2} \]
\end{document}

Related symbols

• Arctangent\arctan
• Arcsine\arcsin
• Arccotangent\text{arccot}
• Cosecant\csc
• Arcsecant\text{arcsec}
• Secant\sec

Frequently asked questions

How do I write Arccosine in LaTeX?

Type \arccos in math mode, for example $\arcsin x + \arccos x = \frac{\pi}{2}$. It works in plain LaTeX without loading any package.

Which package do I need for \arccos?

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

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

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