This is my first post on math.stackexchange (sorry if meta people remove the Hello (sometimes we do that over on stackoverflow ;P)!
I have a system wherein I know that the output is a sine wave, with a known frequency. My objective is to find the approximate (x,y) of the first peak (i.e., find the phase shift of the signal). An important point is that I do not need to know y, or the amplitude, of this peak. Essentially, I can poll the system at a given angular shift (represented by x), and receive a y value in return. I start with zero points, and want to poll the minimum number of x points in order to be able to know where to poll to receive a max y value.
I believe that I can describe the sine wave with only two points, yet I do not know how to calculate this (it's on a motion controller, so I have quite limited functionality). My thoughts so far: phase = -sin^-1(y) - wt + 2*pi*n, but I don't know how to easily fit this with two points.
Once I know the fitted sine wave, I will be able to determine which x should yield a max amplitude peak y, and then subsequently poll the x location.
If this can be done, the final solution would account for noise in the system (i.e. each y point polled will be within a given tolerance... thus, the two or more points polled to fit the sine wave would cause additive errors...), but I'll cross that bridge when I come to it.
Thanks! I think it's a pretty interesting problem :) Let me know if you need any further clarification!