Prove of Rotation Formulas (1)

Lesson#4
Prove of Rotation Formulas (1)
Prove that
X = x cos theta + y sin theta
Y = -x sin theta + y cos theta
PROOF:
If the axes Ox and Oy are rotated about the origin (origin remaining unaltered) through an angle theta, the new axes are OX and OY. If a point P has coordinates (X,Y) referred to xy-system then it has coordinates (X,Y) referred to the rotated XY-system.
Introduction to Analytical Geometry
Chapter No 4
Exercise No 4.2
Mathematics
part 4