8. In 3-D, the Cartesian coordinates are given by the following formulas in terms of the spherical coordinates: x = psin($) cos(0), y = psin($) sin(0), z = pcos($). Find the determinant of the Jacobian matrix. State why this determinant is zero for = ki where k is any integer. Find the inverse transformation, which gives the formulas for (p, (, 0) as functions of (x, y, z). Find the determinant of the Jacobian matrix of the inverse transformation. Finally, show that the product of the two determinants is one