A circular wheel of radius 50cm starts from rest and turns through an angle 2θ about its centre. At a certain instant the condition cos2θ=21 is satisfied.
(i) Determine the least positive value of θ (in radians).
(ii) Express in degrees the total angle through which the wheel has turned at this instant.
(iii) Compute the length of the arc described by a point on the rim of the wheel during this turn.
(iv) If the wheel continues rotating in the same direction until it next satisfies cos2θ=21, find the additional arc length traced out in that time.