Find the length of the curve.
-The circle $r = 6 \sin \theta$
A) $6 \pi$
B) $12 \pi$
C) $36 \pi$
D) $3 \pi$

Question

Quizplus · Accepted Answer

The equation $r = 6 \sin \theta$ represents a circle with a diameter of 6 units in polar coordinates. The length of the curve, which is the circumference of the circle, is given by $C = 2\pi r$, where $r$ is the radius of the circle. Since the diameter is 6, the radius $r$ is $6/2 = 3$. Therefore, the circumference $C = 2\pi(3) = 6\pi$.

Find the Length of the Curve r=6sin⁡θr = 6 \sin \thetar=6sinθ

Find the Length of the Curve $r = 6 \sin \theta$