Solve the problem.
-Find the length of each petal of the polar curve $r = 8 - 3 \sin 4 \theta$. Note that this means the distance from the pole to the farthest point on the petal, not the arc length.
A) 3
B) 5
C) 8
D) 11

Question

Quizplus · Accepted Answer

The length of each petal of the polar curve $r = 8 - 3 \sin 4 \theta$ is found by determining the maximum value of $r$. Since $\sin 4 \theta$ varies between -1 and 1, the maximum value of $r$ occurs when $\sin 4 \theta = 1$, giving $r = 8 - 3(1) = 5$. However, to find the distance from the pole to the farthest point on the petal, we consider the maximum deviation from the average radius, which is $8$. The maximum deviation occurs at $r = 8 - 3(-1) = 11$, making the correct answer 11.

Solve the Problem r=8−3sin⁡4θr = 8 - 3 \sin 4 \thetar=8−3sin4θ

Solve the Problem $r = 8 - 3 \sin 4 \theta$