Example 1. Find polar coordinates of point determined by Cartesian coordinates M=(1,1).

Solution. Polar coordinate system is determined by (P=S,o=x,ϕ), polar coordinates of point M are in the form M=(ρ,ϕ), where

ρ = | S M | = 1 2 + 1 2 = 2

and

ϕ = arcsin x ρ = arcsin 1 2 = π 4
M = ( 2 , π 4 )
ex1
Figure 1: Polar coordinates of point M