Sketch the Astroid y(t) = (cos³(t), sin³(t)). Calculate its tangent vector at each point. At which points is the tangent vector 0?
2. The attempt at a solution
I'm not sure how to go about graphing parametric equations. I calculated the tangent vector:
y'(t) = (-3cos²(t)sin(t), 3sin²(t)cos(t)) and this equals 0 whenever sin(t) = 0 or cos(t) = 0. I have the solution to this quesiton and it says that the points at which y'(t) = 0 correspond to the 4 cusps of the astroid. But I don't even see why this is true. Why is the y'(t) = 0 at (0,1) and (0,-1)? Shouldn't they be undefined?
So could someone please help me out? Maybe tell me what is the general way of graphing parametric equations?