# If sin theta < 0 and tan theta > 0, then in what quadrant is the angle theta?

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Alan P. Share
Apr 15, 2015

The image below indicates the Quadrants in which each of the 3 basic trig functions are positive (sometimes this is called the CAST diagram)

$\sin \left(\theta\right)$ is negative in Q3 and Q4
$\tan \left(\theta\right)$ is positive in Q1 and Q3

Therefore $\theta$ must be in Q3.

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