parametric arc length is given by

I suppose this is what they are getting at. To graph this in parametric, your calculator must be in parametric mode. Parametrically, this is an ellipse, not an astroid. Unless I am missing something. The convention normally used is t instead if theta. Theta is commonly used when dealing with polar coordinates. Even in polar coordinates, this is a rose and not an astroid.

Please do not tell me you mean and did not use ^ to mean power.