Precalculus: Concepts Through Functions, A Unit Circle Approach to Trigonometry (3rd Edition)

Published by Pearson
ISBN 10: 0-32193-104-1
ISBN 13: 978-0-32193-104-7

Chapter 5 - Trigonometric Functions - Section 5.1 Angles and Their Measures - 5.1 Assess Your Understanding - Page 386: 78


$6.283 \text{ meters}$

Work Step by Step

$\because s = r \theta$ where $s$: Length of the arc of the circle $r$: Radius of the circle $\theta$: Central angle that subtends the arc (in radians) Converting $\theta$ from degrees to radians: $$\theta = 120 \times \dfrac{\pi}{180}= \dfrac{2 \pi}{3} \text{ radians}$$ Using the formula above gives: $s = r \theta $ $s = 3 \times \dfrac{2 \pi}{3} \approx \boxed{6.283 \text{ meters}}$
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