Thank you both Dragan and Vinux!

I was afraid that since "B" is where it is in the f(x)=AcosBx that it could not be solved using least-squares [i.e. looking for the equivalent of the estimates for A=SUM(x^2)SUM(y)-SUM(x)SUM(y)/N(SUM(x^2)-(SUM(x))^2 and B=... for the basic equation f(x)=A+Bx but just from the f(x)=AcosBx] and must be estimated numerically. Vinux, I've tried something similar to what you've suggested following the form of the derivation A and B for the OLS solution. Reading your you solution, I think I might have screwed up when I went through it so thank for the feedback and I will give your approach a try.

I've been convinced for a few days now that there is an analytical solution for f(x)=AcosBx using OLS but I'm beginning to agree that it's not possible. That should probably have been obvious to me from the outset given that I'm looking for cosBx as opposed to Bcosx. Out of curiosity, do either of you or anyone else have a sense of how the problem might be solved using something like logistic regression, etc.? (I have less experience with this and don't have a good sense of the utility of this type of approach in this case). Or will I be barking up a similar tree?

Thank you!