Answer
$\text{Quadrant III}$
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 $x<0 \text{ and } \text{\theta} \gt 0$, then $y\lt 0$
Note that points in Quadrant III have $y\lt 0 \text{ and } x<0$
Thus, $\theta \in \text{Quadrant III}$.
