Example 3. Find cylindrical coordinates of point determined by Cartesian coordinates M=(0,1,4).

Solution. Cylindrical coordinate system is determined by

( P = O , o = x , O y , y x , O z , z x y )

Cylindrical coordinates of point M are in the form M=(ρ,ϕ,z), where

ρ = 0 2 + ( 1 ) 2 = 1
y < 0, ϕ = 2 π arccos 0 1 = 2 π π 2 = 3 π 2
z = 4

and

M = ( 1, 3 π 2 ,4 )
ex3
Figure 1: Cylindrical coordinates of point M