Theta lies in which quadrant?

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If $\sin \theta = -\frac{\sqrt 3}2 $and $\tan \theta = \sqrt 3$, then theta lies in which quadrant?

I guess $\sin \theta$ is in the $IV$ quadrant and $\tan \theta$ is in the $III$ quadrant. But I didn't understand further part? Please let me know.

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1 Answer

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Your $\sin\theta$ is negative, which means III or IV quadrant. Your $\tan\theta$ is positive. Since $\tan\theta=\frac{\sin\theta}{\cos\theta}$, it means that $\cos\theta=-\frac{1}{2}$ - negative. Thus $\theta$ is in III quadrant

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