How would I answer this?

http://tinypic.com/view.php?pic=qy5s0i&s=6

Question

How would I answer this?

http://tinypic.com/view.php?pic=qy5s0i&s=6

anonymous · Answer

@Chelsea04 no o:

anonymous · Answer

Well 120 degrees is 1/3 the circle.

The circumference of a circle is 2pi*r, which in this case is 9.

The arc length will be 1/3 * 2 * pi * 9 = 6pi

anonymous · Answer

@Chelsea04 you're kidding right? My logic is confusing? Because using the law of sines unnecessarily will be of great help. Why don't we just evaluate the arc length of the circle as a line integral from t = 0 to t = 2pi/3? I think that's MUCH better.

Ratios are obvious. There is no need to unnecessarily complicate things.

anonymous · Answer

I already did! If you are curious then the circle can be represented as x^2 + y^2 = 81. This can be reparametrized as r(t) = 9<cost,sint>. The arc length is the line integral from 0 to 2pi/3 of |r'(t)|dt which is eactly, hm. 6pi. Is that complicated enough? Or should I extend this to the triple integral and take level curves of four-dimensional objects?

anonymous · Answer

ehh...chill
you're really getting overworked...