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Math Help - [SOLVED] Trig Equation

  1. #1
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    [SOLVED] Trig Equation

    Hello,

    For  \Theta  \epsilon [-2pi, 2pi] find all solutions of the trigonometric equation 2sin2  \Theta - tan  \Theta = 0.
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  2. #2
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    <br /> <br />
2 sin 2 \theta - tan \theta = 0<br />

    = <br /> <br />
4 sin  \theta cos \theta - \frac {sin \theta}{cos \theta}  = 0<br />

    = <br /> <br />
(sin \theta ) \frac{ 4 cos^2 \theta - 1 }{cos \theta}  = 0<br />

    = <br /> <br />
\frac { (sin \theta )(2 cos \theta - 1 )(2 cos \theta + 1 ) }{cos \theta}  = 0<br />

    = <br /> <br />
\frac { 4(sin \theta )( cos \theta - \frac{1}{2} )( cos \theta + \frac{1}{2} ) }{cos \theta}  = 0<br />

    Check where the numerator is 0.
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  3. #3
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    Darn, I can't quite figure it out. Where does the numerator equal 0?
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  4. #4
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    Quote Originally Posted by OVechkin8 View Post
    Darn, I can't quite figure it out. Where does the numerator equal 0?
    If you have some number in the form 4ABC = 0, this will be true:

    • if the first term, A, equals zero;
    • if the second term, B, equals zero; OR
    • if the third term, C, equals zero.


    So above, at least one of your zeros will be at the place the first term, \sin \Theta, equals zero. The rest follow similar logic.
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  5. #5
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    Quote Originally Posted by OVechkin8 View Post
    Darn, I can't quite figure it out. Where does the numerator equal 0?
    where \sin{\theta} = 0 , \cos{\theta} = \frac{1}{2} , and \cos{\theta} = -\frac{1}{2}

    look at your unit circle.
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  6. #6
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    Ohh, I got it guys, THANKS!
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