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Math Help - Trigonometric Equation

  1. #1
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    Trigonometric Equation

    0^o \leq x \leq 360^o

    Solve this equation in terms of the angle of x
    <br />
cot^2x-\sqrt{3}cotx=0<br />
    Last edited by acevipa; March 28th 2008 at 11:09 PM.
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  2. #2
    Moo
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    Hello,

    Let y be cot x.

    The problem is now to solve y^2 - \sqrt{3} y = 0

    -> y=0 \ \text{or} \ y=\sqrt{3}

    Between 0 and 180 the cot function is decreasing. So there is one and only one value verifying y=0 in this interval. And the function is pi(180)-periodic.

    cot x = 0 when x=90 or 270 (because cot x = cos(x)/sin(x))

    We know that \cos(30)=\sqrt{3}/2 and \sin(30)=1/2
    -> cot(30)=\sqrt{3}

    By the property of the periodicity, cot(210)=cot(210)=\sqrt{3} too

    Solutions are S=\{0;30;90;210;270\}
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