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

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

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Answer 1 · 2015-04-15T22:58:58

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

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

Therefore $theta$ must be in Q3.

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

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