CALCULUS CHECK MY ANSWER POLAR CURVES NEED HELP ASAP PLS!

Question

What is distance around the graph of r = 3 sin θ ? (4 points)

ANSWER CHOICES

I CHOSE THIS	3π
	9π
	12π
	72π

Answer 1

Let s = arc length and Θ = the angle subtended.

So, if s = rΘ and r = 3sinΘ, then s = 3ΘsinΘ

If the angle rotates pi/2, half of the arc length is encompassed. So,

(1/2)s = 3(pi/2)sin(pi/2) = 3pi/2 then s = 2(3pi/2) = 3pi