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 asks how to solve for $A$, $B$, $\omega$ and $\varphi$. – joriki Nov 30 '12 at 08:50