Find the length of the entire perimeter of the region inside r=10sinθ but outside r=3.

Question

 Find the length of the entire perimeter of the region inside  but outside .

I got 10(π - 2arcsin(3/10)) but that is wrong.

Answer 1

Draw a figure of the 2 intersecting circles, one with radius of 3 and one with radius of 5.

Find the intersection points (sin θ=.3).

Then use simple plane geometry to find the necessary arc length and don't neglect to make use of obvious symmetry!