Recall that spherical coordinates on R 3 are given by (r; ; ) where r is the radial distance, is the polar angle 2 [0; ] and is the azimuthal angle 2 [0; 2): Using these coordinates we have x = r sin cos y = r sin sin z = r cos The standard Euclidean metric on R 3 is given by ds2 = dx2 + dy2 + dz2 . Show that in the above coordinates this is given by ds2 = dr2 + r 2 d2 + r 2 sin2 d2 :