Multiple Representations in Polar Coordinates

Multiple coordinate sets for a point account for periodicity, causing $r = 2\cos\theta$ to form a complete circle rather than just an arc, as each point has infinite representations.

Considering multiple coordinates ensures the graph is three-dimensional, allowing $r = 2\cos\theta$ to form a sphere instead of a circle.

Multiple coordinate sets are needed to plot discontinuities, making $r = 2\cos\theta$ a series of disconnected points rather than a continuous curve.

Considering multiple coordinates reveals that $r = 2\cos\theta$ actually forms a spiral, not a closed shape, due to the infinite nature of angle measures.