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:(adsbygoogle = window.adsbygoogle || []).push({});

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

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

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