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Math Help - Compound Angle Formula

  1. #1
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    Compound Angle Formula

    A question I have for my college maths assignment is ....

    Show that sin(x+60)+sin(x+60)= sinx using the compound angle formula. Verify this by performing the calculations with the following angle, 0, 60 and 120.

    [All numbers are degrees in the question.]

    Working would be really appreciated and thank you in advanced.

    Ben
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  2. #2
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    Quote Originally Posted by whitelockben View Post
    A question I have for my college maths assignment is ....

    Show that sin(x+60)+sin(x+60)= sinx using the compound angle formula. Verify this by performing the calculations with the following angle, 0, 60 and 120.

    [All numbers are degrees in the question.]

    Working would be really appreciated and thank you in advanced.

    Ben
    sin(x+60) + sin(x+60) = 2sin(x+60)

    sin(A+B) = sinAcosB + cosAsinB

    A = x
    B=60

    2(sin(x)cos(60) + cos(x)sin(60)) = 2(\frac{sin(x)}{2} + \frac{\sqrt{3}}{2}cos(x) = sin(x)+\sqrt{3}cos(x)

    Sure you typed it correctly?
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  3. #3
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    Sorry yes I did, its actually sin(x+60)+sin(x-60)=sinx .
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  4. #4
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    e^(i*pi)'s Avatar
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    Quote Originally Posted by whitelockben View Post
    Sorry yes I did, its actually sin(x+60)+sin(x-60)=sinx .
    In that case we have

    sin(A\pm B) = sinAcosB \pm cosAsinB

    From the unit circle: cos(60) = \frac{1}{2} and sin(60) = \frac{\sqrt3}{2}

    sin(x)cos(60)+cos(x)sin(60) + [sin(x)cos(60) - cos(x)sin(60)]  = 2sin(x)cos(60) = sin(x)
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