Answer
$214^{\circ}$
Work Step by Step
Given-
$\csc\theta$ = - $1.7876$ , $\theta$ belongs to Q III
We will find reference angle of $\theta$ first, using calculator in degree mode by the$\frac{1}{x}$ and $\sin^{-1}$ key with the positive value $1.7876$ as $\sin\theta$ = $\frac{1}{\csc\theta}$
$1.7876$ → $\frac{1}{x}$ → $\sin^{-1}$→→ 34.014954239
i.e. reference angle of $\theta$ = $34.014954239^{\circ}$
The desired angle $\theta$ is in Q III, whose reference angle is $34.014954239^{\circ}$.
Also $0^{\circ}\leq \theta\lt 360^{\circ}$
Therefore-
$\theta$ = $180^{\circ} + 34.014954239^{\circ}$
= $214.01495424^{\circ}$
= $214^{\circ}$
(to the nearest tenth of a degree)
