For each patch, find the coordinates of the unit size tangent vectors a, b at P = (0, 1, 0) in the direction of the equator and meridian line (there are two opposite directions in each case. Make a choice, but be careful to use the same in both patches).

x = sin() cos(), y = sin() sin(), z = cos()

x = u, y = 1 u ² v ², z = v