Question

Spherical to Cartesian transformation

\[f(r,\theta ,\phi )=\frac{C\sin\phi \cos\theta}{r^3}\]

Answer 1

wikipedia says I must use

\[x=r \, \sin\theta \, \cos\varphi\]\[y=r \, \sin\theta \, \sin\varphi\]\[z=r \, \cos\theta\] but I don't really see how this is useful. I feel like it would be more useful to have \(r, \theta\) and \(\phi\) isolated and then plug those in. When I do I get \[f(x,y,z)=\sin\left( \arctan{\frac{y}{x}}\right )\frac{z}{(x^2+y^2+z^2)^2}\]which is quite messy.