2 points and instantaneous phase sufficient to estimate amplitude and frequency of sinusoid? If you have 2 points (x1y1,x2y2) in a Cartesian grid, there are an infinite amount of sinusoids that pass through them. But if you are also given the instantaneous phase (Th0) in radians or degrees at that point, is that sufficient to estimate the amplitude and frequency of the sinusoid that passes through these 2 points? And is there a way to find a formula f(x1y1,x2y2,Th0) where you can simply plug in these 3 variables which returns the amplitude and phase of the sinusoid, so you don't have to look it up in a table? Thanks.
An additional requirement is that the two points not be aliased in terms of their equivalent sampling rate relative to the frequency of the sinusoid.  The distance between the two points can't be a equal or greater than half the period of the sinusoid, or the solution could be ambiguous.