JEE Main & Advanced Mathematics Inverse Trigonometric Functions Domain and Range of Inverse Trigonometric Functions

     

Function	Domain (D)	Range (R)
\[{{\sin }^{-1}}x\]	\[-1\le x\le 1\] or \[[-1,\,1]\,\]	\[-\frac{\pi }{2}\le \theta \le \frac{\pi }{2}\] or \[\left[ -\frac{\pi }{2},\,\frac{\pi }{2} \right]\]
\[{{\cos }^{-1}}x\]	\[-1\le x\le 1\] or \[[-1,\,1]\]	\[0\le \theta \le \pi \]or \[[0,\,\pi ]\]
\[{{\tan }^{-1}}x\]	\[-\infty <x<\infty \] i.e., \[x\in R\] or \[(-\infty ,\,\infty )\]	\[-\frac{\pi }{2}<\theta <\frac{\pi }{2}\] or \[\left( -\frac{\pi }{2},\,\frac{\pi }{2} \right)\]
\[{{\cot }^{-1}}x\]	\[-\infty <x<\infty \] i.e., \[x\in R\] or \[(-\infty ,\,\infty )\]	\[0<\theta <\pi \] or \[(0,\,\pi )\]
\[{{\sec }^{-1}}x\]	\[x\le -1,\,x\ge 1\]                      or  \[(-\infty ,\,-1]\cup \,[1,\,\infty )\]	\[\theta \ne \frac{\pi }{2},\,0\le \theta \le \pi \] or \[\left[ 0,\,\frac{\pi }{2} \right)\,\cup \left( \frac{\pi }{2},\,\pi  \right]\]
\[\text{cose}{{\text{c}}^{-1}}x\]	\[x\le -1,\,x\ge 1\] or \[(-\infty ,\,-1]\,\cup \,[1,\,\infty )\]	\[\theta \ne 0,\,-\frac{\pi }{2}\le \theta \le \frac{\pi }{2}\] or \[\left[ -\frac{\pi }{2},\,0 \right)\,\cup \left( 0,\,\frac{\pi }{2} \right]\]