These coordinate system are two equivalent ways of representing a vector. Use the coordinate system that is most appropriate for the problem.
Cartesian coordinates: A = (Ax,Ay) = Ax + Ay
Polar coordinates: A = Ar if the vector begins at the origin. Sometimes we write such a vector as A =(r,θ) Here θ is the angle between the positive x-axis and A. More generally, A = (Ar,Aθ); (see transparency.
Conversion between cartesian and polar coordinates: see transparency.