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JEE • Mathematics

Inverse Trigonometric Functions

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table

Principal Domains and Ranges

The principal value table is stored exactly as visually verified from the handbook.

Function	Domain	Range
$\sin^{-1}x$	$-1\le x\le1$	$-\frac{\pi}{2}\le y\le\frac{\pi}{2}$
$\cos^{-1}x$	$-1\le x\le1$	$0\le y\le\pi$
$\tan^{-1}x$	$x\in\mathbb{R}$	$-\frac{\pi}{2}<y<\frac{\pi}{2}$
$\cosec^{-1}x$	$x\le-1\text{ or }x\ge1$	$-\frac{\pi}{2}\le y\le\frac{\pi}{2},\ y\ne0$
$\sec^{-1}x$	$x\le-1\text{ or }x\ge1$	$0\le y\le\pi,\ y\ne\frac{\pi}{2}$
$\cot^{-1}x$	$x\in\mathbb{R}$	$0<y<\pi$

Variables & Notation

$x$

variable or observation