Sketch the polar curve with the given equation.

Question

Quizplus · Accepted Answer

The polar curve with equation $r = 11\cos^3	heta$ is a limacon with a loop. The loop is formed when $\cos 	heta$ is negative, which happens when $\frac{\pi}{2} < 	heta < \frac{3\pi}{2}$. Option A is incorrect because $r$ should be in terms of $\cos 	heta$ and not $\sin 	heta$. Option C is incorrect because $r$ would only be non-negative when $	heta$ is an odd multiple of $\frac{\pi}{2}$, which would not create a loop. Option D is incorrect because it does not have a loop.

Sketch the Polar Curve with the Given Equation