Today I had learned cycloid which well parametarized with t as (t-sint, 1-cost)
What looks peculiar with this notation is that coordinate y is differentiated form of x.
Thus I had questioned myself "any coordinate (x(t), dx(t)/dt) Cycloid?" which mean there exist unique circle that denotes cycloidic movement.
+additional question : Is there any way to close out t and make the cycloid notation in a form of y=f(x)?