Answer the following questions related to the radian measure of angles.
(i) Define one radian.
(ii) Using the definition in part (i), state the exact measure (in radians only) of the angles subtended at the centre of a circle by
(a) a semicircle,
(b) a quarter-circle, and
(c) one complete revolution.
(iii) State any two reasons why, in higher mathematics, the radian measure is preferred over the degree measure.