Trigonometry (10th Edition)

Published by Pearson
ISBN 10: 0321671775
ISBN 13: 978-0-32167-177-6

Chapter 3 - Radian Measure and the Unit Circle - Section 3.1 Radian Measure - 3.1 Exercises: 89

Answer

(a) $4\pi$ radians. (b) $\frac{2\pi}{3}$ radians

Work Step by Step

(a) The hour hand on a clock makes two complete rotations in $24$ hours as one complete rotation represents $12$ hours. One complete rotation is represented by $360^{\circ}$ or $2\pi$ radians. Therefore, two complete rotations represent $2(2\pi)=4\pi$ radians. (b) Since one complete rotation of $12$ hours represents $2\pi$ radians, $4$ hours represent one-third of this time period. Therefore, $4$ hours represent $\frac{1}{3}\times2\pi=\frac{2\pi}{3}$ radians.
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