## Trigonometry (11th Edition) Clone

arccsc$(-\displaystyle \frac{1}{2})$ is not defined.
Inverse Cosecant Function: $y=\csc^{-1}x$ or $y=$ arccsc $x$ means that $x=\csc y$, for $-\displaystyle \frac{\pi}{2} \leq y \leq \frac{\pi}{2}$ , $y\neq 0$. ----------------- If there exists a y such that $\displaystyle \csc y=-\frac{1}{2}$, then, sine being reciprocal to csc, $\displaystyle \sin y=-\frac{2}{1}=-2$, which can not be for any y, since the range of sine is $[-1,1].$ So, arccsc$(-\displaystyle \frac{1}{2})$ is not defined.