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Math Help - In which quadrant must theta lie if it satisfies the following inequalities?

  1. #1
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    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!
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  2. #2
    Super Member bigwave's Avatar
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    by observation

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

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

    however once \cos(\theta) goes into Q4 (-)(+) then the \sin(\theta)\cos(\theta) goes negative
    so that leaves just Q3 (-)(-)
    Last edited by bigwave; August 30th 2010 at 10:37 AM. Reason: wording
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