Why there is a constraint on $\phi$ which is $0\leq \phi \leq \pi?$ Why is it not $0 \leq \phi \leq 2\pi?$
My next question:-Let $P = (a,\theta,\phi)$ be a point in spherical coordinates, with a > 0 and $0<\phi < \pi.$ Then P lies on the sphere $\rho = a.$ Since $0 < \phi < \pi,$ the line segment from the origin to P can be extended to intersect the cylinder given by r = a (in cylindrical coordinates).
Find the cylindrical coordinates of that point of intersection.
How to answer this question? Answer given by author is $(a,\theta, a\cot\phi)$ and it is correct.
