# Which quadrant does θ lie, if sin θ > 0 and sec θ < 0?

Apr 5, 2018

II

#### Explanation:

$\sin \left(\theta\right) > 0$ In quadrants I and II

$\sec \left(\theta\right) = \frac{1}{\cos} \left(\theta\right)$

$\cos \left(\theta\right) < 0$ in quadrants II and III

So the quadrant where $\sin \left(\theta\right) > 0 \mathmr{and} \frac{1}{\cos} \left(\theta\right) < 0$ is:

II