Some exercises with coordinate systems a) find the conversion from spherical (aka "polar") to cartesian coordinates, i. e. the functions z(r, 0, 6), y(r,0,) and 2(r, 0, 0). also find the inverse functions, r(r, y, 2), etc. b) find the conversion from cylindrical to cartesian coordinates, i. e. the functions r(p, o, 2), etc. also find the inverse functions, p(x, y, 2), etc e) a particle starting from the origin moves in the f direction with velocity vo and polar angles o and 0, such that = v, f. expressõ in cartesian coordinates.