Polar circles and limaçons

Build reliable sketches of polar circles, cardioids and limaçons from angle samples, symmetry and radial behavior. This precalculus practice set includes a plotted curve and asks how signs, coefficients and sine-versus-cosine choices affect orientation, pole crossings and inner loops.

Fourteen single-select and multiselect questions progress from circle geometry to limaçon classification and interpretation of negative radii. Worked explanations check key points and distinguish minimum signed radius from minimum distance to the pole. Parameter signs are stated when classification rules are used. A failed algebraic symmetry test is treated as inconclusive rather than as a proof that symmetry is absent.