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Find two solutions for Cosine theta = 1/2 for

  1. Jul 4, 2011 #1
    Find two solutions for Cosine theta = 1/2 for....

    1. Find two solutions for Cosine theta = 1/2 for 0 degrees less than or equal to theta less than or equal to 360 degrees. Express answers in degrees and radians.


    2. Relevant equations



    3. I know that Cosine theta = 1/2 gives you 60 degrees which is also pie/3 radians. I dont know what the other solution is though. Can anyone help?
     
  2. jcsd
  3. Jul 4, 2011 #2

    eumyang

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    Re: Find two solutions for Cosine theta = 1/2 for....

    Are you familiar with reference angles? See http://www.analyzemath.com/Angle/reference_angle.html" [Broken].
     
    Last edited by a moderator: May 5, 2017
  4. Jul 4, 2011 #3
    Re: Find two solutions for Cosine theta = 1/2 for....

    Im familiar with reference angles. I just didnt know to use them but since you mentioned it, what comes to mind is taking 60 degrees from 360 degrees. That leaves me with 300 degrees. From there, i dont know how to proceed.
     
  5. Jul 5, 2011 #4
    Re: Find two solutions for Cosine theta = 1/2 for....

    Well whats cos 300?
     
  6. Jul 5, 2011 #5
    Re: Find two solutions for Cosine theta = 1/2 for....

    yea after a while i figured it out. cos 300= 1/2
     
  7. Jul 5, 2011 #6

    eumyang

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    Re: Find two solutions for Cosine theta = 1/2 for....

    No, it's not. cos 300 = -0.02209661927868394268907560278956...

    Or perhaps you meant cos 300° = 1/2. The degree sign is important. Without it, I have to assume you mean radians. Speaking of which, don't forget that you were asked to find answers in degrees and radians.
     
  8. Jul 6, 2011 #7
    Re: Find two solutions for Cosine theta = 1/2 for....

    maybe i can help
    since cos 60 = 1/2 , i'll use x as theta
    => cos x = cos 60

    1. cos x = 60 + k.360
    => x = 60

    2. cos theta = -60 + k.360
    => x = 300

    in degree x = {60, 300}
    in radian x = {1/3 pi rad, 5/3 pi rad}
     
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