Inverse Trigonometric Functions
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 | \((0, \pi)\) |