Polar Graphs

Circles, cardioids and limaçons

An interactive lesson with 6 steps, about 5 minutes: you predict, drag and solve, with instant feedback on every answer. It runs in your browser and needs JavaScript.

What you’ll learn

• A polar graph r = f(θ) is drawn by a sweeping radius.
• r = constant is a circle; θ = constant is a line through the pole.
• Limaçons r = 1 + b cos θ: dimpled (b < 1), cardioid (b = 1), inner loop (b > 1).

Steps

1. Sweeping a radius
2. Find the cardioid
3. A hidden circle
4. A constant angle
5. Where the inner loop starts
6. A cardioid standing up