I have a general understanding of calculating arc length, but this one's a real curve ball.
So, I need to find the exact length of $r=3\sin(θ)$ on $0 ≤ θ ≤ π/3$
So the way I've thought of approaching it is by using some handy formulas:
$$r^2 = x^2 + y^2$$
and $$y=r\sin(θ)$$
So we start off with
$$r=3\sin(θ)$$
$$r^2 = 3r\sin(θ)$$ $$(x^2 + y^2)^{1/2} = 3y$$
$$x^2 + y^2 = 9(y^2)$$
$$x^2 = 8y^2$$
$$(1/8)^{1/2}x = y$$
Then, from that I use the integration formula to find length. Am I even close to being right on this one?