Question Cartesian coordinates ask how far east and how far north. Polar coordinates ask: how far from a lighthouse, and at what compass angle? The pair (r, θ) relocates the same plane with a different grammar. Circles centered at the origin become r = constant. Rays from the origin become θ = constant. Roses and limaçon curves appear as simple formulas in r(θ) that look wild in x and y.
Consider
Convert between polar and Cartesian coordinates Recognize r = const and θ = const geometrically Identify common polar curves (circles, roses, limaçons) Allow negative r and non-unique θ when interpreting plots
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Lighthouse nav: distance r, compass angle θ x = r cos θ y = r sin θ r² = x² + y²
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