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For what points $(x_i, y_i) \in \mathbb{R}^2, i=1..4 $ we can find real $A, B, \omega, \varphi$ such that: $A + B \sin (\omega x_i + \varphi) = y_i$?

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    [This closely related question](http://math.stackexchange.com/questions/59007) asks how to solve for $A$, $B$, $\omega$ and $\varphi$.2012-11-30

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