This discussion focuses on the conversion between spherical and cylindrical coordinates. The established formulas are: for spherical to cylindrical, r = (ρ² + z²)^(1/2), θ = arcsin(ρ/(ρ² + z²)^(1/2)), and ψ = ψ; and for cylindrical to spherical, ρ = r sin(θ), z = r cos(θ), and ψ = ψ. A suggestion was made to use θ = arctan(ρ/z) instead of arcsin for a potentially clearer approach. The provided solutions are confirmed to be correct.
PREREQUISITESStudents in mathematics or physics, educators teaching coordinate systems, and anyone involved in fields requiring spatial transformations.
armolinasf said: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