Trigonometric and hyperbolic functions

This table describes how to type trigonometric and hyperbolic functions, along with usage examples (including the typeset equivalent.) If the expression you need is not listed, please define your own and explain the meaning of your notation.

Expression Description Examples

$\displaystyle \sin{x},\:\cos{x},\:\tan{x}$

$\displaystyle \csc{x},\:\sec{x},\:\cot{x}$

The trigonometric functions, in radians unless otherwise stated.

$\displaystyle \sin{\frac{\pi}{2}}=1$

$\displaystyle \cos{\frac{\pi}{4}}=\frac{\sqrt{2}}{2}$

sin(pi/2) = 1
cos(pi/4) = [sqrt(2)]/2

$\displaystyle \arcsin{x},\:\arccos{x}, etc.$

or

sin^-1(x), cos^-1(x), etc. The inverse trigonometric functions.

$\displaystyle \arcsin{1}=\frac{\pi}{2}$

$\displaystyle \arccos{\frac{\sqrt{2}}{2}}=\frac{\pi}{4}$

arcsin(1) = (pi/2)
arccos[sqrt(2)/2] = (pi/4)

$\displaystyle \sinh{x},\:\cosh{x},\:\tanh{x},\: etc.$

The hyperbolic functions.

$\displaystyle \sinh{x}=\frac{e^x-e^{-x}}{2}$

$\displaystyle \cosh{x}=\frac{e^x+e^{-x}}{2}$

sinh(x) = (e^x - e^-x) / 2
cosh(x) = (e^x + e^-x) / 2

sinh^-1(x), cosh^-1(x), etc. The inverse hyperbolic functions. sinh^-1(x) = ln[x + sqrt(x^2 + 1)]

cosh^-1(x) = ln[x + sqrt(x^2 - 1)]

Expression	Description	Examples
$\displaystyle \sin{x},\:\cos{x},\:\tan{x}$ $\displaystyle \csc{x},\:\sec{x},\:\cot{x}$	The trigonometric functions, in radians unless otherwise stated.	$\displaystyle \sin{\frac{\pi}{2}}=1$ $\displaystyle \cos{\frac{\pi}{4}}=\frac{\sqrt{2}}{2}$ sin(pi/2) = 1 cos(pi/4) = [sqrt(2)]/2
$\displaystyle \arcsin{x},\:\arccos{x}, etc.$ or sin^-1(x), cos^-1(x), etc.	The inverse trigonometric functions.	$\displaystyle \arcsin{1}=\frac{\pi}{2}$ $\displaystyle \arccos{\frac{\sqrt{2}}{2}}=\frac{\pi}{4}$ arcsin(1) = (pi/2) arccos[sqrt(2)/2] = (pi/4)
$\displaystyle \sinh{x},\:\cosh{x},\:\tanh{x},\: etc.$	The hyperbolic functions.	$\displaystyle \sinh{x}=\frac{e^x-e^{-x}}{2}$ $\displaystyle \cosh{x}=\frac{e^x+e^{-x}}{2}$ sinh(x) = (e^x - e^-x) / 2 cosh(x) = (e^x + e^-x) / 2
sinh^-1(x), cosh^-1(x), etc.	The inverse hyperbolic functions.	sinh^-1(x) = ln[x + sqrt(x^2 + 1)] cosh^-1(x) = ln[x + sqrt(x^2 - 1)]