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Math Help - y = sine x = cos x

  1. #1
    Newbie zacharyrod's Avatar
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    Exclamation y = sine x = cos x

    If y = A*sin(Bx + C) + D is substituted as y = -1.5 sin(x + π/4) + 4, what

    would the cosine function be in order to match the graph of said sine

    function?
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  2. #2
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    e^(i*pi)'s Avatar
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    Quote Originally Posted by zacharyrod View Post
    If y = A*sin(Bx + C) + D is substituted as y = -1.5 sin(x + π/4) + 4, what

    would the cosine function be in order to match the graph of said sine

    function?
    Note that  \cos(x) = \sin \left(x - \frac{\pi}{2}\right). You can show this using the subtraction formula for sin. In terms of the graphs it means the graph of cos(x) is shifted by pi/2 to the right on the x axis

    Only C would change as it's a phase difference

    -1.5\cos \left(x + \frac{\pi}{4} - \frac{\pi}{2}\right) + 4 = -1.5\cos \left(x - \frac{\pi}{4}\right) + 4
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  3. #3
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    -1.5cos(x-π/4)+4
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