Answer
$\text{Quadrant IV}$
Work Step by Step
$P= (x,y) \text{ is the point on the unit circle corresponding to } \theta$
We have:
$\sin{\theta} = y<0 $
$\tan{\theta} = \dfrac{y}{x} <0$
Since $y<0$ and $\tan{\theta}\lt 0$, then $x\gt 0$
Note that points in Quadrant IV have $y<0 \text{ and } x>0$.
$\therefore \theta \in \text{Quadrant IV}$
