Convert the point from cylindrical coordinates to spherical coordinates.
(2, 2π/3, −2)
(ρ, θ, φ) = ??????

Question

Convert the point from cylindrical coordinates to spherical coordinates.
(2, 2π/3, −2)
(ρ, θ, φ) = ??????

anonymous · Answer

I got $$2\sqrt{2},\frac{ 2\pi }{ 3 },\frac{ \pi }{ 4 }$$ Why is that wrong?

zepdrix · Answer

Bahhh I had to look up the conversions.. I couldn't quite remember...
I should draw out the sphere and try to figure that out sometime >.<

$$\Large\rm \rho =\sqrt{x^2+y^2+z^2}$$I'm also coming up with $\Large\rm 2\sqrt{2}$, ok cool.

I have something different for my $\Large\rm \phi$ though, hmmm let's see...

zepdrix · Answer

$$\Large\rm z=\rho \cos \phi \qquad\to\qquad \cos \phi =\frac{z}{\rho}$$$$\Large\rm \cos \phi =\frac{-2}{2}=-1$$

Which gives ussssss... $\Large\rm \pi$ I think?
Mmm I better check my work...
Oh oh I plugged in the r from the cylindrical coordinates for phi! Hah!

Plugging in the ACTUAL phi,
ya ya ya ya ya ya ya ya.. ok ok it makes sense now.
It's still negative though isn't it?$$\Large\rm \cos \phi =-\frac{\sqrt2}{2}$$Which would be uhhh 3pi/4?