sin θ = r → arcsin r = sin − 1 r = θ {\displaystyle \sin {\theta }=r\to \arcsin {r}=\sin ^{-1}{r}=\theta } . The domain of y = arcsin x θ {\displaystyle y=\arcsin {x}\theta } is [ − 1 , 1 ] {\displaystyle [-1,1]} , and its range is [ − π 2 , π 2 ] {\displaystyle [{\frac {-\pi }{2}},{\frac {\pi }{2}}]} .
cos θ = r → arccos r = cos − 1 r = θ {\displaystyle \cos {\theta }=r\to \arccos {r}=\cos ^{-1}{r}=\theta }
tan θ = r → arctan r = tan − 1 r = θ {\displaystyle \tan {\theta }=r\to \arctan {r}=\tan ^{-1}{r}=\theta }
csc θ = r → arccsc r = csc − 1 r = θ {\displaystyle \csc {\theta }=r\to \operatorname {arccsc} {r}=\csc ^{-1}{r}=\theta }
sec θ = r → arcsec r = sec − 1 r = θ {\displaystyle \sec {\theta }=r\to \operatorname {arcsec} {r}=\sec ^{-1}{r}=\theta }
Examples:
<math> \sin{\frac{\pi}{4}} = \frac{\sqrt{2}}{2} \to \arcsin{\frac{\sqrt{2}}{2}} = \frac{\pi}{4}
. The domain of 
is ![{\displaystyle [-1,1]}](https://wikimedia.org/api/rest_v1/media/math/render/svg/51e3b7f14a6f70e614728c583409a0b9a8b9de01)
, and its range is ![{\displaystyle [{\frac {-\pi }{2}},{\frac {\pi }{2}}]}](https://wikimedia.org/api/rest_v1/media/math/render/svg/9dc7f3c869691e842d0daf385da660f75dbb66c3)
.
