Answer the following with reference to angles measured in radians.
(i) Define the radian measure of an angle.
(ii) Prove that if an arc of length s on a circle of radius r subtends an angle θ at the centre, then θ=rs when θ is expressed in radians.
(iii) An arc whose length equals the radius of the circle is drawn. Find the magnitude of the angle subtended by this arc at the centre in degrees.