This was my attempt at showing the need for a high sample rate if you are going to get a real feel for what is going on with the data. If you sample this cosine wave every four seconds, you would think it was a straight line. You would have to sample it every 1 second to get the correct notion that it is a cosine wave. It is the same reason we are reducing the ∆t from 9 seconds down to a ∆t of 1 second. It gives us a much better feel for the changing velocity.