Inverse Trigonometric Functions

	domain	range
$\displaystyle y=\arcsin{x}\quad\iff\quad x=\sin{y}$	$\displaystyle [-1,1]$	$\displaystyle \left[-\frac{\pi}{2},\frac{\pi}{2}\right]$
$\displaystyle y=\arccos{x}\quad\iff\quad x=\cos{y}$	$\displaystyle [-1,1]$	$\displaystyle [0,\pi]$
$\displaystyle y=\arctan{x}\quad\iff\quad x=\tan{y}$	$\displaystyle (-\infty,\infty)$	$\displaystyle \left(-\frac{\pi}{2},\frac{\pi}{2}\right)$
$\displaystyle y=\arccot {x}\quad\iff\quad x=\cot{y}$	$\displaystyle (-\infty,\infty)^1$	$\displaystyle (0,\pi)^1$
$\displaystyle y=\arcsec {x}\quad\iff\quad x=\sec{y}$	$\displaystyle (-\infty,-1] \cup [1,\infty)^1$	$\displaystyle \left[0,\frac{\pi}{2}\right) \cup \left(\frac{\pi}{2},\pi\right]^1$
$\displaystyle y=\arccsc {x}\quad\iff\quad x=\csc{y}$	$\displaystyle (-\infty,-1] \cup [1,\infty)^1$	$\displaystyle \left[-\frac{\pi}{2},0\right) \cup \left(0,\frac{\pi}{2}\right]^1$

There is an alternative notation which uses what appears to be, but is not, an exponent of -1. For example, using this notation sin $^{-1}$ = arcsin, not csc.