The question required the plot of the polar graph for $\;r=4\cos\theta\sin^2\theta\;$.
How to explain why there is no curve on the left side of the $y$-axis? Should I show all the calculations to explain it?
2026-03-27 02:37:40.1774579060
How to explain why there is no curve to the left of the $y$-axis?
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It is because $\cos\theta$ becomes negative on the left of the $y$-axis, which results in negative $r$. That means that $r$ maps from 2nd quadrant to the 4th, and from the 3rd one to the 1st. You may convince yourself by direct substitution that $r(\theta)$ and $r(\theta+\pi)$ map to the same point.