Question

Convert the (10, 90, 60) coordinates to Cartesian coordinates which are in Spherical coordinates.

(a) (5, 8.66, 10)

(b) (5, 8.66, 0)

(c) (10, 5, 8.66)

(d) (0, 5, 8.66)

I have been asked this question by my school teacher while I was bunking the class.

I want to ask this question from Conversion from Cartesian, Cylindrical and Spherical Coordinates in section Vector Differential Calculus of Engineering Mathematics

Answer 1

The correct choice is (b) (5, 8.66, 0)

To elaborate: The Spherical coordinates is of the form (r, θ, φ) and Cartesian coordinates is of the form (x, y, z) where x = r sin⁡θ cos⁡ϕ and y = rsin⁡θ sin⁡ϕ and z=rcos⁡θ. Now, substituting the values for r as 10, θ as 90, and φ as 60, substituting the values we get

x = 10 sin90 cos60 = 5

y = 10 sin90 sin60 = 8.66

z = 10 cos90 = 0.