(i) Explain why the radian measure of an angle is equal to the ratio of the length of the arc subtended by the angle at the centre of a circle to the radius of the circle.
(ii) Using the fact stated in part (i), show that the radian measure of one complete revolution is 2π.
(iii) Decide which angle is larger—1 radian or 60∘—and justify your answer without using a calculator.