Polar Graphs Math Example 2

Solution

1. 1
   This has the form $r = a + b\cos\theta$ with $a = b = 2$. When $a = b$, the curve is a cardioid.
2. 2
   Maximum $r$: when $\cos\theta = 1$ ($\theta = 0$), $r = 4$. Minimum $r$: when $\cos\theta = -1$ ($\theta = \pi$), $r = 0$.
3. 3
   The curve passes through the origin when $\theta = \pi$ and has its farthest point at $(4, 0)$.
4. 4
   The graph is symmetric about the polar axis (the $x$-axis) because replacing $\theta$ with $-\theta$ gives the same equation.