# Thread: In which quadrant must theta lie if it satisfies the following inequalities?

1. ## In which quadrant must theta lie if it satisfies the following inequalities?

In which quadrant must theta lie if it satisfies the following inequalities:

sin(theta)<0, sin(theta)cos(theta)>0

I'm at a loss as to how to solve this. Could someone please push me in the right direction?

Thank you!

2. ## by observation

$\displaystyle \sin(\theta)<0, \sin(\theta)\cos(\theta)>0$

to keep $\displaystyle \sin(\theta),$ negative it has to stay in Q3 or Q4

however once $\displaystyle \cos(\theta)$ goes into Q4 (-)(+) then the $\displaystyle \sin(\theta)\cos(\theta)$goes negative
so that leaves just Q3 (-)(-)