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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?

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    After $r^2=3r\sin\theta$, the next line should be $x^2+y^2=3y$, without the square root, since the left-hand side was $r^2$.2011-05-27

5 Answers 5