## Trigonometry (11th Edition) Clone

$-30^o$
The value of $\theta$ must be in the interval $[-90^o, 0^o) \cup (0^o, 90^o]$. $\theta=\csc^{-1}{\left(-2\right)}$ means that $\csc{\theta} = -2$. Since cosecant is the reciprocal of sine, then $\csc{\theta} = -2$ means $\sin{\theta}=-0.5$. Note that $\sin{30^o} = 0.5$. Since $\sin(-x)=-\sin{x}$, then $\sin{(-30^o)}=-\sin{30^o} = -0.5$ Thus, $\csc^{-1}{\left(-2\right)}=-30^o$