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Thread: sin a sinx+ b cosx

  1. November 19th 2009, 06:19 AM #1
    Oasis1993
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    sin a sinx+ b cosx

    Hey.
    The question is find the value of R and the value of A.

    sinx+ 2cosx = Rcos(x-A)

    i can find R which is square root of 5, but i keep getting 1.11 for A and the answer is 0,46 (radians)

    can anyone help?
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  2. November 19th 2009, 07:35 AM #2
    Grandad
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    Hello Oasis1993
    Quote Originally Posted by Oasis1993 View Post
    Hey.
    The question is find the value of R and the value of A.

    sinx+ 2cosx = Rcos(x-A)

    i can find R which is square root of 5, but i keep getting 1.11 for A and the answer is 0,46 (radians)

    can anyone help?
    R\cos(x-A) = R\cos x \cos A + R \sin x \sin A=\sin x + 2\cos x

    \Rightarrow R\sin A = 1,\;R\cos A = 2

    \Rightarrow \tan A =\tfrac12

    \Rightarrow A = 0.46...

    Grandad
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