Which of the following is equivalent to ${\csc }^{-1}\left(y\right)$ for $y\ne 0$?

${\sin }^{-1}\left(\frac{1}{y}\right)$

${\cos }^{-1}\left(\frac{1}{y}\right)$

${\tan }^{-1}\left(\frac{1}{y}\right)$

${\cot }^{-1}\left(\frac{1}{y}\right)$