# Arc Length Question

1. Oct 7, 2008

### DarkSamurai

1. The problem statement, all variables and given/known data
Find the arc length of r(t) = cos(t)^3 i + sin(t)^3 j
from t = 0 to t = 2 * Pi

It's a hypocycloid that's four cusped.

2. Relevant equations
$$s = \int\sqrt{x'^2 + y'^2}$$

3. The attempt at a solution
x = cos(t)^3
y = sin(t)^3

x' = -3cos(t)^2*sin(t)
y' = 3sin(t)^2*cos(t)

$$\sqrt{x'^2 + y'^2}$$ = 3* $$\sqrt{cos(t)^4*sin(t)^2 + sin(t)^4*cos(t)^2}$$

That simplifies to $$s = \int 3*\sqrt{1}$$

So the answer is 6*Pi, but for some reason Maple throws out 6.

2. Oct 7, 2008

### Dick

The radical doesn't simplify to 1. Check that again.