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Math Help - Compound Angle Question

  1. #1
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    Compound Angle Question

    Determine Sin(x+y)

    If Sinx = 4/5 Cosy = 12/13

    Therefore the following is true.
    sinx = 4/5
    cosx = (+/-)3/5
    siny = (+/-)5/12
    cosy = 12/13
    Angle X can be in Quadrant 1 or 2
    Angle Y can be in Quadrant 1 or 4

    s(x+y) = (4/5)(12/3) + (3/5)(5/12)
    = 63/65

    My Question is, that is this the only solution or do i have to plug in the negative values of cosx and siny in the equation to get different answers?

    Thanks Alot
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  2. #2
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    Re: Compound Angle Question

    i have to plug in the negative values of cosx and siny in the equation to get different answers
    you do if the quadrants for angles x and y were not specified ...
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  3. #3
    Senior Member MaxJasper's Avatar
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    Lightbulb Re: Compound Angle Question

    x=\left\{\sin ^{-1}\left(\frac{4}{5}\right),\pi -\sin ^{-1}\left(\frac{4}{5}\right)\right\}

    y=\left\{\cos ^{-1}\left(\frac{12}{13}\right),2 \pi -\cos ^{-1}\left(\frac{12}{13}\right)\right\}
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