sin θ = r → arcsin r = sin − 1 r = θ {\displaystyle \sin {\theta }=r\to \arcsin {r}=\sin ^{-1}{r}=\theta }
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:
sin π 4 = sin 3 π 4 = s q r t 2 2 → arcsin s q r t 2 2 = π 4 {\displaystyle \sin {\frac {\pi }{4}}=\sin {\frac {3\pi }{4}}={\frac {sqrt{2}}{2}}\to \arcsin {\frac {sqrt{2}}{2}}={\frac {\pi }{4}}} , 3 π 4 {\displaystyle {\frac {3\pi }{4}}}
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