Quote:
Originally Posted by Axonymous
I calculated what I think is the best approximation by minimizing the derivative over a of the integral of the sine function minus the line y=ax. When I compare this to the result of my simulation, there's a difference of about 30% between the two possible values for a.

Which problem is that for?
Like the lecture and the book, you consider a best fit for two points (least squares), and then average over all sets of two points (but not two of the same point). Then a in this case, or (a,b) in the book case, is/are the average over all such pairs of points.
I might believe that is 30% different from the one you mention.
You could also minimize the integral of the square of the sin()ax.