Question

Convert the point (3,4,5) from Cartesian to spherical coordinates

(a) (7.07,45⁰,53⁰)

(b) (0.707,45⁰,53⁰)

(c) (7.07,54⁰,63⁰)

(d) (0.707,54⁰,63⁰)

The question was posed to me during an online interview.

The question is from Spherical Coordinate System in chapter Coordinate Systems and Transforms of Electromagnetic Theory

Answer 1

Right option is (a) (7.07,45⁰,53⁰)

Best explanation: r = √(x^2+y^2+z^2) = √50 = 7.07

Θ = cos^-1(z/r) = cos^-1(5/5√2) = 45⁰

Φ = tan^-1(y/x) = tan^-1(4/3) = 53⁰.