Question

How do you graph `r = 3 + 3 cos theta`?

Answer 1

Tabulation shows the curve passes successively through the polar (6, 0), (3, `pi/2`), (0, `pi`), (3, 3`pi`/2) and (6, 2`pi`). A smooth curved join gives the cardioid (heart-like) closed curve

Explanation:

r is periodic with period 2`pi`. cos `theta` = cos (`-theta`). So, the curve is symmetrical about the initial line `theta` = 0. The curve has a cusp at the pole (0, 0). A major portion lie in the first and fourth quadrants..