- #1
DarkSamurai
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Homework Statement
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.
Homework Equations
[tex]s = \int\sqrt{x'^2 + y'^2}[/tex]
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)
[tex]\sqrt{x'^2 + y'^2}[/tex] = 3* [tex]\sqrt{cos(t)^4*sin(t)^2 + sin(t)^4*cos(t)^2}[/tex]
That simplifies to [tex]s = \int 3*\sqrt{1}[/tex]
So the answer is 6*Pi, but for some reason Maple throws out 6.