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Thread: Solving for Theta in Sin(Theta)=1/2 Using The Unit Circle

  1. #1
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    Solving for Theta in Sin(Theta)=1/2 Using The Unit Circle

    I've been using Brightstorm recently to prepare for the next lesson, it's great but occasionally you run into some questions and I don't believe they get answered any time soon.

    I'm watching this video in particular and I am stuck with the second solution for sin(theta)=1/2
    Solving Trigonometric Equations (Video)
    Solving for Theta in Sin(Theta)=1/2 Using The Unit Circle-capturebt.png(Picture)

    If (pi) radians is equal to 180 degrees and all three angles of all three triangles is equal to 180 degrees, why isn't the supplement angle (pi)-(2(theta))?
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  2. #2
    Super Member bigwave's Avatar
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    Cool

    not sure if this helps but if

    \sin{\theta} =  \frac{1}{2}
    then

    \sin^{-1}{\left(\frac{1}{2}\right)} = \frac{\pi}{6} or \frac{5\pi}{6}
    Last edited by bigwave; Jul 8th 2010 at 01:58 PM. Reason: latex
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  3. #3
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    That is the result he also got using (pi) - (theta). However, for me, it visual doesn't make sense. The angle of the center triangle must (in my eyes at least) (pi) - (2theta). Is the supplementary angle different?

    Edit: Looking at again, it looks like the second solution includes the first angle as well which would make sense. Now I don't understand the supplement angle. Checking Google as of now...
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  4. #4
    Super Member bigwave's Avatar
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    Cool angle between

    Quote Originally Posted by Altermeris View Post
    That is the result he also got using (pi) - (theta). However, for me, it visual doesn't make sense. The angle of the center triangle must (in my eyes at least) (pi) - (2theta). Is the supplementary angle different?
    by the angle of the center triangle do you mean the angle between \frac{\pi}{6} and \frac{5\pi}{6}

    if so then \pi - 2\theta will give the answer

    however, I think supplement refers to pairs of angles between \pi

    the center angle is not a supplement to \theta
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