University Calculus: Early Transcendentals (3rd Edition)

Published by Pearson
ISBN 10: 0321999584
ISBN 13: 978-0-32199-958-0

Chapter 1 - Section 1.3 - Trigonometric Functions - Exercises - Page 27: 1


The length of the arc is (a) $8\pi$ (m) (b) $\frac{55\pi}{9}$ (m)

Work Step by Step

To find out the length of the arc, we need to employ the formula: $$s = r\theta$$ $s$: the length of the arc $r$: radius of the circle $\theta$: the central angle of the arc (in radians) (a) $r=10m, \theta=\frac{4\pi}{5}$ radians The length of the arc would be $$s=10\times\frac{4\pi}{5}$$ $$s=8\pi (m)$$ (b) $r=10m, \theta=110^\circ$ - First, we need to change $\theta$ back to radians: $$\theta=110^\circ\times\frac{\pi}{180^\circ}=\frac{11\pi}{18}(radians)$$ The length of the arc would be $$s=10\times\frac{11\pi}{18}$$ $$s=\frac{55\pi}{9} (m)$$
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