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

1 Answer
A. S. Adikesavan
Feb 18, 2016

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..

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