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Fitting a cosine function to an inflection point and a point with known derivative

  1. Oct 30, 2012 #1
    I am trying to fit a cosine function to two points knowing that the first is an inflection point (e.g. a trough) and also knowing the gradient at the second. I have a gut feeling this has a unique solution it just needs the right identities and massaging but as of yet I haven't found the way:

    Consider a cosine function:

    y(x)=A.cos(B.x)+C

    and derivative:

    y'(x)=B.A.sin(B.x)

    and given:

    y(0)=Y0
    y(X1)=Y1
    y'(X1)=DY1

    where X1, Y0,Y1 and DY1 are known constants

    find the analytical solution for A,B and C

    My boundless gratitude to anyone who can solve this.

    Adam
     
  2. jcsd
  3. Oct 30, 2012 #2

    mfb

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    Staff: Mentor

    Re: Fitting a cosine function to an inflection point and a point with known derivativ

    In general, I would expect that your solution is not unique.

    Using the inflection point, you know where y''(x1)=0, this will give you several possible values for B. In addition, y(x1)=C fixes C.
    For each value of B, you can then calculate the gradient at your second point and solve that for A.
     
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