Answer
$326.63^{\circ}$
Work Step by Step
Here, we have $\sin \theta =-0.55; 270^{\circ} \lt \theta \lt 360^{\circ}$
$\theta'=\sin^{-1} (-0.55) \approx -33.37^{\circ}$
This angle $\theta'$ is in the $II$ quadrant .
We need to get the co-terminal angle in the range of $ 270^{\circ} \lt \theta \lt 360^{\circ}$. We will just have to add $360^{\circ}$.
Then we have
$ \theta=-33.37^{\circ}+360^{\circ} \approx 326.63^{\circ}$
