4. The curve in R² traced out by $\vec{r}(t) = (5 + \sin(10t))\cos(t)\vec{i} + (5 + \sin(10t))\sin(t)\vec{j}$, $0 \le t \le 2\pi$, approximates the perimeter of a sprocket. Draw a picture of the curve. Hint: The motion has the form $\langle R(t)\cos(t), R(t)\sin(t) \rangle$, $0 \le t \le 2\pi$, which is like drawing a circle counter-clockwise while varying the radius with time. Compute the perimeter of the sprocket using numerical integration. Assume the coordinates have units of centimeters (cm).