Example 6. Find Cartesian coordinates of point determined by spherical coordinates M=(2,3π2,π3).

Solution. Cartesian coordinate system is determined by

( O = S , x = p 1 , O y , y x , z = p 2 )

Cartesian coordinates of point M are in the form M=(x,y,z), where

x = ρ cos ϕ sin ζ = 2 cos 3 π 2 sin π 3 = 0
y = ρ sin ϕ sin ζ = 2 sin 3 π 2 sin π 3 = 3
z = ρ cos ζ = 2 cos π 3 = 1

and

M = ( 0, 3 ,1 )

ex6
Figure 1: Cartesian coordinates of point M