4. (Framing plane curves and defining signed curvature) If o: R - R2, we may use the perp operator from the "Square-Wheeled car" homework to define a frame: T(s) = a'(s), N(s) = T(s). Definition. If a (s) is a plane curve, the signed curvature is k4 (8) := (T(s), N(s)). (1) Suppose that o(s) = (rcos , r sin #), the circle of radius r parametrizatio wise. Compute the signed curvature: K+ (S) = Show your work below.Remember that (r, y) = (-y, x). `Notice that unlike the curvature k(s) for space curves, which is equal to ||7"(s) || and hence always non-negative, the signed curvature ky (s) can have either sign because the dot product which defines it can be negative.(2) Now consider B(s) = (r cos , -rsin #), the circle of radius r parametrizationise. Compute the signed curvature: K+ (S ) = Show your work below