Cosecant in LaTeX (\csc)

Where it is used

Cosecant, the reciprocal of sine, set as an upright operator.

\csc\theta = 1/\sin\theta, undefined at integer multiples of \pi. Its derivative is \frac{d}{dx}\csc x = -\csc x\cot x, and the identity 1 + \cot^2 x = \csc^2 x completes the Pythagorean trio. Some books, especially older British ones, abbreviate it cosec; that form needs \operatorname{cosec}. A common error is writing \sin^{-1} x when \csc x is meant: the superscript -1 denotes the inverse function arcsine, not the reciprocal. Powers attach right after the command, as in \csc^2 x, with the argument following.

Minimal compilable example

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

\documentclass{article}
\begin{document}
Cosecant: $\csc$

\[ \frac{d}{dx} \csc x = -\csc x \cot x \]
\end{document}

Related symbols

• Arcsine\arcsin
• Secant\sec
• Arccosine\arccos
• Cotangent\cot
• Arctangent\arctan
• Tangent\tan

Frequently asked questions

How do I write Cosecant in LaTeX?

Type \csc in math mode, for example $\frac{d}{dx} \csc x = -\csc x \cot x$. It works in plain LaTeX without loading any package.

Which package do I need for \csc?

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

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

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