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Solving Trigonomic Inequalites

  1. Oct 25, 2008 #1
    Find where cosθ = -0.8660, where (0 degrees ≤ θ < 540 degrees)

    I am not sure how to solve this problem

    I did: cosθ + 0.8660 = 0

    Then I am not sure what to do
  2. jcsd
  3. Oct 25, 2008 #2


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    Staff Emeritus
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    Well, use a calculator! That will give you the "principal value". Then use the fact that cosine is periodic with period 360 degrees and that cos(360- t)= cos(t) to find all other values.
  4. Oct 25, 2008 #3
    [tex]\cos \theta = -0.8660[/tex]
    [tex]\theta = \arccos -0.8660[/tex]

    That's as far as you can go if you want to stay exact. But you can calculate the answer using a calculator (there is probably something like 'cos-1' key on it, that's the arccos key.)

    However, if you've worked with trigonometry for some time you will find that you recognize some numbers. For example: 0.8660 looks like it's probably meant to be [tex]\frac{1}{2} \sqrt(3) = 0.866025404...[/tex]

    The arccos of -1/2 sqrt(3) however IS exact (try it on your calc!):

    Note, this is only one answer. If you allow theta to be in the range you specified you get more answers!
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