Graph the polar equation.
-$$r = 3 ( 2 + 2 \sin \theta )$$

Question

Quizplus · Accepted Answer

The graph of $r=3(2+2\sin	heta)$ is a rose curve with $4$ petals since the coefficient of $	heta$ is $2$. The maximum value of $\sin	heta$ is $1$, which occurs at $	heta=\frac{\pi}{2},\frac{5\pi}{2},\frac{9\pi}{2},\frac{13\pi}{2}$, and the minimum is $-1$, which occurs $	heta=-\frac{\pi}{2},\frac{3\pi}{2},\frac{7\pi}{2},\frac{11\pi}{2}$. Thus, the graph has $4$ petals at $	heta=\frac{\pi}{2},\frac{5\pi}{2},\frac{9\pi}{2},\frac{13\pi}{2}$ and $r$ is minimal at $	heta=\pi,\pi,3\pi,3\pi$.

The correct graph is shown in choice $	extbf{(C)}$.

Graph the Polar Equation r=3(2+2sin⁡θ)r = 3 ( 2 + 2 \sin \theta )r=3(2+2sinθ)

Graph the Polar Equation $r = 3 ( 2 + 2 \sin \theta )$