AP Calculus BC glossary

Polar curve

A polar curve expresses distance from the origin as a function of the angle. Familiar shapes include circles, cardioids, limacons, and rose curves, and a negative r means the point is plotted in the opposite direction from the angle.

A rose curve $r = a\cos(k\theta)$ has $k$ petals when $k$ is odd and $2k$ when $k$ is even, which is the standard fact tested about petal counting.

The mistake

Assuming a negative r is impossible. A negative radius reflects the point through the origin, and ignoring that loses whole sections of many curves.

Appears in: Unit 9: Parametric, Polar, and Vector (BC)