The parametrization of the sphere:

$\displaystyle {\bf x}\,(u^1,u^2) = (r \cos u^2 \cos u^1,\ r \cos u^2 \sin u^1,\ r \sin u^2)$

$\displaystyle 0 \leq u^1 < 2\pi,\ \ \ -\frac{\pi}2 \leq u^2 \leq \frac{\pi}2$

appears in my book without explanation. Any help on how to derive it? (I played with it and found the coordinates correspond to latitude and longitude).