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