The hour hand of a large clock moves continuously. Starting from the 12 o’clock position it turns through 97∘25′50′′ in the first hour, then an additional 1.4 radians in the second hour, and finally −32∘18′ in the third hour due to a reverse motion caused by a malfunction.
(i) Convert each of the three rotations to radians, correct to four significant figures.
(ii) Calculate the total angular displacement after the three hours in radians.
(iii) Determine the smallest positive angle coterminal with the displacement found in part (ii) and express it in degrees–minutes–seconds.