Expressing Spherical coordinates in terms of cylindrical

[armolinasf]

Homework Statement

I'm trying to express spherical coordinates in terms of cylindrical and vice versa. I would appreciate it if someone could give me some feedback on my attempt at a solution. Thanks for the help!

The Attempt at a Solution

Spherical(cylindrical)

r=(ρ^2+z^2)^(1/2)
θ=arcsin(ρ/(ρ^2+z^2)^(1/2))
ψ=ψ

Cylindrical(Spherical)

ρ=rsinθ
z=rcosθ
ψ=ψ

 

[Chestermiller]

Homework Statement

I'm trying to express spherical coordinates in terms of cylindrical and vice versa. I would appreciate it if someone could give me some feedback on my attempt at a solution. Thanks for the help!

The Attempt at a Solution

Spherical(cylindrical)

r=(ρ^2+z^2)^(1/2)
θ=arcsin(ρ/(ρ^2+z^2)^(1/2))
ψ=ψ

Cylindrical(Spherical)

ρ=rsinθ
z=rcosθ
ψ=ψ

What you've done is already correct. What more are you asking? Incidentally, you might want to use θ=arctan(ρ/z) instead of θ=arcsin(ρ/(ρ^2+z^2)^(1/2)), but that is a matter of taste.