| \(f\) | Restricted Domain | \(f^{-1}\) | Domain |
|---|---|---|---|
| \(f(x) =\sin x\) | \(\left[ -\dfrac{\pi }{2},\dfrac{\pi }{2}\right] \) | \(f^{-1}( x) =\sin ^{-1}x\) | \([-1,1] \) |
| \(f(x) =\cos x\) | \([0,\pi] \) | \(f^{-1}( x) =\cos ^{-1}x\) | \([-1,1] \) |
| \(f(x) =\tan x\) | \(\left( -\dfrac{\pi }{2},\dfrac{\pi }{2}\right) \) | \(f^{-1}( x) =\tan ^{-1}x\) | \((-\infty ,\infty) \) |
| \(f(x) =\csc x\) | \(\left(-\pi, -\dfrac{\pi}{2}\right]\cup \left(0, \dfrac{\pi}{2}\right]\) | \( f^{-1}( x) =\csc ^{-1}x\) | \(|x| ≥ 1\) |
| \(f(x) =\sec x\) | \(\left[0, \dfrac{\pi}{2}\right)\cup \left[\pi, \dfrac{3\pi}{2}\right)\) | \( f^{-1}(x) =\sec ^{-1}x\) | \(|x| ≥ 1\) |
| \(f(x) =\cot x\) | \((0,\;\pi) \) | \(f^{-1}( x) =\cot ^{-1}x\) | \((-\infty ,\infty) \) |