Consider the family of curves defined by the parametric equations $$x = \sin(t)(c-\sin(t)),\quad y=\cos(t)(c-\sin(t)).$$ Note that as $c$ changes, the shape of the curve changes. Identify the transitional values of $c$. In other words, list the values of $c$ for which the basic shape of the curve changes.

In listing these numbers, give them in increasing order. Type an upper-case "N" in any unused answer fields.

Smallest transitional value: $c =$

Next smallest transitional value: $c =$

Next smallest transitional value: $c =$

Next smallest transitional value: $c =$

Next smallest transitional value: $c =$