Convert the point from cylindrical coordinates to spherical coordinates. (6, 𝜋, 8)

Question

Convert the point from cylindrical coordinates to spherical coordinates.

(6, 𝜋, 8)

(𝜌, 𝜃, φ) = ( )

Answer 1

ρ = sqrt(r² + z²) = 10

The physics convention appears to be θ is the elevation angle (This is frustrating as this means that the spherical Φ = cylindrical θ = π)

and θ = cos^-1(z/ ρ) = cos^-1(8/10) = 36.87° (with vertical = 0°)