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Math Help - Trig problem (cos)

  1. #1
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    Trig problem (cos)

    Hi I really don't know to do this problem.

    The equation cos(3x) = 1/2

    has two solutions between 0 and 120 degrees. The smaller is _____ degrees and the larger is _______ degrees.

    Am I suppose to take cos(pi/3) / 3 and thats my answer?
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  2. #2
    MHF Contributor
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    Quote Originally Posted by killasnake
    Hi I really don't know to do this problem.

    The equation cos(3x) = 1/2

    has two solutions between 0 and 120 degrees. The smaller is _____ degrees and the larger is _______ degrees.

    Am I suppose to take cos(pi/3) / 3 and thats my answer?
    No, you are not supposed to do that.
    Instead, you are supposed to get the the arccosine of (1/2), and equate those to 3x to find x.

    cos(3x) = 1/2
    That means the cosine of an angle, here it is 3x, is positive 1/2.
    In the 4 quadrants, where is cosine value positive?
    Cosine is positive where the x-coordinate is positive. The x-coordinate is positive to the right of the y-axis, or at the 1st and 4th quadrants. Hence, the angle 3x is in the 1st or 4th quadrant.

    cos(3x) = 1/2
    3x = arccos(1/2)
    3x = 60 degrees in the 1st quadrant.
    3x = 360 -60 = 300 degrees in the 4th quadrant.

    Therefore, x = 60/3 = 20 degrees.
    or, x = 300/3 = 100 degrees.
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  3. #3
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    oh! Thank you for the explanation.
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