Why does Desmos draw different perimeters for the graphs of $$r=\cos(2\theta)$$ and $$r\le\cos(2\theta)$$ (2 leaves versus 4 leaves)? Why do the numbers of leaves differ?
$r=\cos(2\theta)$
$r\le\cos(2\theta)$
Why does Desmos outlines $r=\cos(2\theta)$ differently from $r\le\cos(2\theta)$
desmosgraphing-functionspolar coordinates
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Best Answer
In the second case, you are throwing out the cases where $\cos(2\theta)$ goes negative. In particular, the vertical petals are drawn when $r$ goes negative. For example, the lower petal corresponds to $\frac{\pi}{4}<\theta<\frac{3\pi}{4}$.