How do you graph $r = 3 + 3 cos θ$ $r = 3 + 3 cos theta$ ?

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How do you graph $r = 3 + 3 cos θ$ $r = 3 + 3 cos theta$ ?

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Answer 1 · 2016-02-18T12:00:20

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

Explanation:

r is periodic with period 2 $π$ $pi$ . cos $θ$ $theta$ = cos ( $- θ$ $-theta$ ). So, the curve is symmetrical about the initial line $θ$ $theta$ = 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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How do you graph $r = 3 + 3 cos θ$ $r = 3 + 3 cos theta$ ?

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How do you graph $r = 3 + 3 cos θ$ $r = 3 + 3 cos theta$ ?