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