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Polar Graphs, Limaçons, Lemniscates, ...

Circles:
$$r=r$$ $$r=a\ast cos\theta$$ $$r=a\ast sin\theta$$

Cardioids & Limaçons:
$$r=a+b\ast cos\theta$$ $$r=a+b\ast sin\theta$$

Lemniscates:
$$r=\sqrt{a^2\ast cos(2\theta )}$$ $$r=\sqrt{-a^2\ast cos(2\theta )}$$ $$r=\sqrt{a^2\ast sin(2\theta )}$$ $$r=\sqrt{-a^2\ast sin(2\theta )}$$

Rose curves:
$$r=a\ast cos(n\theta )$$

Archimedes's spiral:
$$r=a\theta$$