You know how to graph a y = sin(x) or y = cos(x) by starting with your 5 key points. But, someone has gone and made it messy by changing the period and doing a phase shift.  How do you figure out your 5 key points for the new, dark side of the force equation?

Please note:  At least one time I say "Phase" when I mean "Period."  Sorry 'bout that...