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: 3

Answer

The length of the arc in the nearest tenth is $8.4$ inch.

Work Step by Step

To find 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) Here we have $\theta=80^\circ$ and diameter $d=12$ inch. - In radians: $\theta=80^\circ\times\frac{\pi}{180^\circ}=\frac{4\pi}{9}$ - The radius of the circle is: $r=\frac{d}{2}=6$ in. So the length of the arc would be: $$s=6\times\frac{4\pi}{9}=\frac{8\pi}{3}$$ $$s\approx8.4(in.)$$
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