Question

Convert Cartesian coordinates (2, 6, 9) to Cylindrical and Spherical Coordinates.

(a) (6.32, 71.565., 6.32) and (11, 71.565., 35.097)

(b) (6.32, 71.565., 9) and (6.32, 71.565., 35.097)

(c) (6.32, 71.565., 6.32) and (6.32, 35.097., 71.565)

(d) (6.32, 71.565., 9) and (11, 35.097., 71.565)

The question was posed to me in an interview.

My question comes from Conversion from Cartesian, Cylindrical and Spherical Coordinates in division Vector Differential Calculus of Engineering Mathematics

Answer 1

Correct answer is (d) (6.32, 71.565., 9) and (11, 35.097., 71.565)

Easy explanation: The Cylindrical coordinates is of the form ( ρ, φ, z) where \(ρ=\sqrt{x^2+y^2} \) and \( φ=tan^{-1}⁡(\frac{y}{x}) \) and z=z where (x, y, z) is the Cartesian coordinates. The Spherical coordinates is of the form (r, θ, φ) where \(r=\sqrt{(a^2+b^2 +c^2 )}, \, θ = tan^{-1}⁡(\frac{\sqrt{x^2+y^2}}{z}) \) and \( φ=tan^{-1}⁡(\frac{y}{x})\). Now, substituting the values for x as 2, y as 6 and z as 9, we get the answer as (6.32, 71.565., 9) and (11, 35.097., 71.565.).