$y = \csc x\;$ [$-\frac{\pi}{2}$, 0) $\cup$ (0, $\frac{\pi}{2}$]

$y = \sec x\;$ [0, $\frac{\pi}{2}$) $\cup$ ($\frac{\pi}{2}, \pi$]

$y = \cot x\;$ (0, $\pi$)

$y = \csc^{-1} x\;$ (-$\infty$, -1] $\cup$ [1, $\infty$)

$y = \sec^{-1} x\;$ (-$\infty$, -1] $\cup$ [1, $\infty$)

$y = \cot^{-1} x\;$ (-$\infty, \infty$)