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Math Help - change to the form Acos(x+w)

  1. #1
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    change to the form Acos(x+w)

    How do you change F(x) = -cosx + sqrt3sint to the form:

    Acos(x+w)

    with A and w both exact values?
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  2. #2
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    Hello JQ2009
    Quote Originally Posted by JQ2009 View Post
    How do you change F(x) = -cosx + sqrt3sint to the form:

    Acos(x+w)

    with A and w both exact values?
    I assume you mean
    F(x)= -\cos x + \sqrt3\sin x
    So, let F(x) = A\cos(x+w). Then:
    -\cos x + \sqrt3\sin x=A\cos(x+w)
    =A\cos x \cos w - A\sin x\sin w
    Compare coefficients of \cos x and \sin x:
    -1 = A\cos w

    \sqrt3 = -A\sin w
    Square and add:
    4 = A^2(\cos^2w+\sin^2w)

    \Rightarrow A = -2 (taking - sign)
    Divide second equation by the first:
    \tan w = \sqrt3

    \Rightarrow w = \pi/3

    \Rightarrow F(x) = -2\cos(x+\pi/3)
    Grandad
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