SOLUTION: Name the quadrant in which the angle &#952; lies. cos&#952;<0, csc&#952;<0

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Question 169158: Name the quadrant in which the angle θ lies. cosθ<0, cscθ<0
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Remember csc%28theta%29=1%2Fsin%28theta%29. So if csc%28theta%29%3C0 then 1%2Fsin%28theta%29%3C0 (ie sine is negative)


So if cosθ<0, then we're dealing with quadrants 2 and 3 (which are the left most quadrants). Also, since 1%2Fsin%28theta%29%3C0 (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 θ lies in quadrant 3.