Question 169158
Remember {{{csc(theta)=1/sin(theta)}}}. So if {{{csc(theta)<0}}} then {{{1/sin(theta)<0}}} (ie sine is negative)



So if cos&#952;<0, then we're dealing with quadrants 2 and 3 (which are the left most quadrants). Also, since {{{1/sin(theta)<0}}} (which means that sine is negative), this means that we're dealing with the lower quadrants 3 and 4. 



Take the two regions and find the intersection, you'll find that the only quadrant that they have in common is quadrant 3. So angle &#952; lies in quadrant 3.