a) Consider the vector field on the circle given by = 2 sin 0. Show that this system has a single-valued potential V(0) i.e., for each point on the circle, there is a well-defined value of V such that = -dV/de. (As usual, 0 and 0+2k are to be regarded as the same point on the circle, for each integer k.) b) Now consider = 1. Show that there is no single-valued potential V(0) for this vector field on the circle. c) Whats the general rule? When does f(0) have a single-valued potential?