A string is wound around a circle and then unwound while being held taut. The curve traced by the point P at the end of the string is called the involute of the circle. If the circle has radius and center 0 and the initial position of P is (r, 0) and if the parameter is θ chosen as in the figure, show that parametric equations of the involute are
x = r (cos θ + θ sin θ) y = r (sin θ - θ cos θ)