Spherical Jacobian Factor

Problem

In spherical coordinates (r, phi, theta) with phi measured from the positive z-axis, the volume element is dV = r^2 * sin(phi) dr dphi dtheta.

Given r and the polar angle phi in radians, return the Jacobian factor r^2 * sin(phi).

Hint

The factor vanishes at the poles where sin(phi) = 0.

case 1

in: [2,1.5707963267948966]

expected: 4

case 2

in: [1,0]

expected: 0

case 3

in: [3,0.5235987755982988]

expected: 4.499999999999999

case 4

in: [0,1]

expected: 0

Starter codePython

def spherical_jacobian(r, phi):
    # Your code here
    pass

4 test cases · run your code against them in the editor