Going Beyond \( x \) and \( y \)

Polar coordinates describe points by how far they are from the origin (\( r \)) and at what angle (\( \theta \)).

• Instead of \( (x, y) \), use \( (r, \theta) \).
• Some curves are easier in polar form, like spirals or roses.

Calculus in Polar Form

• Area inside a polar curve: \( A = \frac{1}{2} \int_{\alpha}^{\beta} [r(\theta)]^2 d\theta \).
• Find slopes and lengths of polar curves.

Cool Connections

Polar graphs appear in radar, biology (shells), and engineering (antenna patterns).