A wheel makes a partial turn of radians

MATHEMATICS · Subjective · A Level · Mathematics · Trigonometry · Trigonometry

Problem

A wheel makes a partial turn of 5.745.74 radians. (i) Express this angular displacement in degree measure correct to two decimal places. (ii) Further express the result of part (i) in degrees–minutes–seconds form, rounding the seconds to the nearest whole number. (iii) If the wheel subsequently turns through an additional 9π10\dfrac{9\pi}{10} radians in the same direction, find the total angular displacement from the starting position in DMS form. Give the final answer to the nearest second.

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