Example 4. Find Cartesian coordinates of point determined by cylindrical coordinates M=(3,π,7).

Solution. Cartesian coordinate system is determined by (O=P,x=o,Oy,yx), Cartesian coordinates of point M are in the form M=(x,y,z), where

x = ρ cos ϕ = 3 cos π = 3
y = ρ sin ϕ = 3 sin π = 0
z = 7

and

M = ( 3,0,7 )

ex4
Figure 1: Cartesian coordinates of point M