Find a piecewise smooth parametric curve to the astroid. The astroid, given by $\phi(\theta) = (cos^3(\theta),sin^3(\theta))$, is not smooth, as we see singular points at 0, pi/2, 3pi/2, and 2pi. However is there a piecewise smooth curve?
$\phi(\theta) = (cos^3(\theta),sin^3(\theta))$
The Attempt at a Solution
I have tried to use the cartesian equation x^(2/3) + y^(2/3) = 1 but that didn't help. I tried to change the periodicity of the cos and sine functions but obviously that was pointless. I thought at one time maybe this is not possible, but I see examples of line integrals over the astroid so it must be piecewise smooth. Can I get a hint?