I know its a little silly, but I got the wrong sign several times. Just to be clear, $z=r\cos(\phi), -\frac{\pi}{2}\leq\phi\leq\frac{\pi}{2}$ when converting from cartesian to spherical. So, how do I determine the sign? Thanks!
Finding the sign of $\phi$ in spherical coordinates
0
$\begingroup$
calculus
coordinate-systems
vector-analysis
spherical-coordinates
-
0I just happen to be a TA in a calculus course this semester and we just got to spherical coordinates. We teach that $0\leq\phi\leq\pi$ and $z=r\cos\phi$. – 2012-06-17
1 Answers
1
The spherical coordinate system I learned has $z=r \cos \theta$ with $0 \le \theta \le \pi$. For that range of $\phi$ you need to use $z=r \sin(\phi)$, in which case you can get the sign. I have seen geographers use this, though they usually use $\lambda$ for latitude