Answer
Quadrant I and IV
Work Step by Step
Case 1- When $\sin\theta$ and $\tan\theta$ both are positive
By Definition I-
$\sin\theta$ =$ \frac{y}{r}$
Given $\sin\theta$ is positive, hence y is positive as r being distance can not be negative. 'y' is positive in Quadrant I and II.
$\tan\theta$ =$ \frac{y}{x}$
If y is positive, x also has to be positive for $\tan\theta$ to be positive. Thus x and y both are positive.
Hence terminal side lies in Quadrant I.
Case 2- When $\sin\theta$ and $\tan\theta$ both are negative
By Definition I-
$\sin\theta$ =$ \frac{y}{r}$
Given $\sin\theta$ 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, x has to be positive for $\tan\theta$ to be negative.
Thus x is positive and y is negative.
Hence terminal side lies in Quadrant IV.
