1.5.1—Polar coordinates

A polar point is written (r,θ), where r is the directed distance from the pole and θ is the angle from the initial line. Cartesian coordinates satisfy x=r cosθ and y=r sinθ.

The same point can have infinitely many representations: (r,θ)=(r,θ+2π) and (−r,θ)=(r,θ+π). Decide whether the problem uses a signed radius or restricts r≥0.

The point (2,π/3) has Cartesian coordinates (1,√3). The representation (−2,4π/3) describes the same point.

Do not treat θ as a length or assume a unique polar pair; angle periodicity and negative r matter.