π,y=arccos⁡xifx=cos⁡y;for−π2<y<π2,y=arctan⁡xifx=tan⁡y;for−π2≤y≤π2,y≠0,y=arccsc⁡xifx=csc⁡y;for0≤y≤π,y≠π2,y=arcsec⁡xifx=sec⁡y;for0<y<π,y=arccot⁡xifx=cot⁡y.{\displaystyle {\begin{matrix}{\mbox{for}}&-{\frac {\pi }{2}}\leq y\leq {\frac {\pi }{2}},&y=\arcsin x&{\mbox{if}}&x=\sin y\,;\\\\{\mbox{for}}&0\leq y\leq \pi ,&y=\arccos x&{\mbox{if}}&x=\cos y\,;\\\\{\mbox{for}}&-{\frac {\pi }{2}}<y<{\frac {\pi }{2}},&y=\arctan x&{\mbox{if}}&x=\tan y\,;\\\\{\mbox{for}}&-{\frac {\pi }{2}}\leq y\leq {\frac {\pi }{2}},y\neq 0,&y=\operatorname {arccsc} x&{\mbox{if}}&x=\csc y\,;\\\\{\mbox{for}}&0\leq y\leq \pi ,y\neq {\frac {\pi }{2}},&y=\operatorname {arcsec} x&{\mbox{if}}&x=\sec y\,;\\\\{\mbox{for}}&0<y<\pi ,&y=\operatorname {arccot