Vectors and Coordinates Emmanuel Branlard January 2011

1

System of coordinates

1.1

The example of Polar vs Cartesian coordinates

Polar to Cartesian: x = r cos θ

(1)

y = r sin θ

(2)

Cartesian coordinates to polar coordinates: r=

θ=

q

y 2 + x2

(3)

  arctan( xy )     y  arctan( x ) + π    y 

arctan( x ) − π

π    2   π   −  2   

0

if if if if if if

x>0 x