Unit 9 – Parametric equations, Polar Coordinates, and Vector-valued Functions

A cycliod with its velocity and acceleration vectors.

Implicit Differentiation of Parametric Equations – where that “extra” dx/dt comes from.

A Vector’s Derivatives – The velocity and acceleration vectors illustrated.

Polar Equations

Polar Equations for AP Calculus – An outline of what to know about polar curves.

Extreme Polar Conditions – Finding extreme values for polar curves.

Addition posts on vector and parametric equations. These eight posts explain how to write complicated curves using vectors. Suitable for precalculus; not required for AP calculus.

Rolling Circles – Roulettes

Epicycloids

Epitrochoids

Hypocycloids and Hypotrochoids

Roulettes and Calculus

Roulettes and Art – 1

Roulettes and Art – 2

Limaçons