domains and ranges

The following table gives the inverse trigonometric function (principal value branches) along with their domains and ranges.

Function Domain Range (Principal Value Branch)
\(sin^{-1}\) \([-1, 1]\) \([-\frac{\pi}{2}, \frac{\pi}{2}]\)
\(cos^{-1}\) \([-1, 1]\) \([0, \pi]\)
\(cosec^{-1}\) \(R - (-1, 1)\) \([-\frac{\pi}{2}, \frac{\pi}{2}] - \{0\}\)
\(sec^{-1}\) \(R - (-1, 1)\) \([0, \pi] - \{\frac{\pi}{2}\}\)
\(tan^{-1}\) R \((-\frac{\pi}{2}, \frac{\pi}{2})\)
\(cot^{-1}\) R \((0, \pi)\)