Answer
Quadrant III
Work Step by Step
By Definition I-
$\sin\theta$ =$ \frac{y}{r}$
$\sin\theta$ is negative, hence y is negative as r being distance can not be negative. 'y' is negative in Quadrant III and IV.
$\tan\theta$ =$ \frac{y}{x}$
If y is negative, then $\tan\theta$ can be negative only when x is also negative.
Therefore x and y both are negative i.e. terminal side lies in Quadrant III
