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Thread: [SOLVED] Trig Equation

  1. #1
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    [SOLVED] Trig Equation

    Hello,

    For $\displaystyle \Theta $ $\displaystyle \epsilon $ [-2pi, 2pi] find all solutions of the trigonometric equation 2sin2 $\displaystyle \Theta $ - tan $\displaystyle \Theta $ = 0.
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  2. #2
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    $\displaystyle

    2 sin 2 \theta - tan \theta = 0
    $

    = $\displaystyle

    4 sin \theta cos \theta - \frac {sin \theta}{cos \theta} = 0
    $

    = $\displaystyle

    (sin \theta ) \frac{ 4 cos^2 \theta - 1 }{cos \theta} = 0
    $

    = $\displaystyle

    \frac { (sin \theta )(2 cos \theta - 1 )(2 cos \theta + 1 ) }{cos \theta} = 0
    $

    = $\displaystyle

    \frac { 4(sin \theta )( cos \theta - \frac{1}{2} )( cos \theta + \frac{1}{2} ) }{cos \theta} = 0
    $

    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, $\displaystyle \sin \Theta$, 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 $\displaystyle \sin{\theta} = 0$ , $\displaystyle \cos{\theta} = \frac{1}{2}$ , and $\displaystyle \cos{\theta} = -\frac{1}{2}$

    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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