(PC2) Polar Regions#

In this lesson we are going to see:

  • how to graph basic polar curves.

  • how to graph polar regions.

Review Videos#


Example 1#

Graph the polar curve given by \(r=2\).

Example 2#

Graph the polar curve given by \(\theta = \dfrac{\pi}{6}\).

Example 3#

Sketch the region of the plane where points satisfy:

\[ 0\leq r \leq 2 \qquad \quad 0 \leq \theta \leq \dfrac{3\pi}{4} \]

Example 4#

Sketch the region of the plane where points satisfy:

\[ 2\leq r \leq 4 \qquad \quad \dfrac{\pi}{3} \leq \theta \leq \dfrac{3\pi}{2} \]

Example 5#

Describe the following region using polar coordinates.

\[ x\geq 0 \qquad \quad x^2+y^2\leq 9 \]