Calculating Polar Curve Length with Period of 3π: r = psin3(θ/3)

[Snoogx]

Homework Statement

Find the length of the polar curve r = psin³(\theta/3)
Hint: The period of the curve is 3\pi

Homework Equations

L = \intsqrt(f(\theta)² + f'(\theta)²)d\theta

The Attempt at a Solution

I know from the hint that 0\leq\theta\geq3\pi

The only problem I have is how do I start this with "p" in the r-equation. Do I treat it as another variable or is it a constant?

 

[fzero]

I would treat p as a constant, you're not given necessary information to solve the problem if it were not.

 

[HallsofIvy]

If p were not a constant, the equation would not define a curve.