Cartesian coordinates and polar coordinates are both simply means of describing a point on the plane. This means that a point or set of points can be described using whatever coordinate system is most convenient. Being able to convert from one form to another is important, as it allows you to restate a problem in a more convenient way.

Neither method is inherently superior; rather, the choice of coordinate systems should be made based on what kind of problem you are attempting to solve.

Polar coordinates are often more useful when examining graphs that encircle the origin one or more times, or when performing rotations or dilations around the origin.

By the end of these quizzes, you'll understand how the polar functions \(r=\cos(k\theta)\) or \(r=\sin(k\theta)\) can be modified in various ways to produce a petal-like design: