In total for both coordinates
x 2 ¼ x 1 cos u þ y 1 sin u
y 2 ¼ Àx 1 sin u þ y 1 cos u
Writing in a matrix form these equations for a clockwise proper rotation of two
coordinates,
cos u sin u
À sin u cos u
!
x 1
y 1
!
¼
x 2
y 2
!
For all three coordinates,
cos u sin u 0
À sin u cos u 0
0
0
1
2
4
3
5
RotaƟon of the y-coordinate
RotaƟon of the z-coordinate
RotaƟon of the x-coordinate
Point P in Cartesian coordinates
1.5 Group Theory
15