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: 86


$9.425 \, m^2$

Work Step by Step

$\because A = \dfrac{1}{2}r^2 \theta$ where $r$: Radius of the circle $\theta$: Central angle that subtends the arc (in radians) $A$: Area of the sector of the circle formed by the central angle $\theta$ Convert $\theta$ from degrees to radians: $$\theta = 120 \times \dfrac{\pi}{180}= \dfrac{2 \pi}{3} \text{ radians}$$ Use the formula above to obtain: $A= \dfrac{1}{2}\times (3)^2 \times \dfrac{2 \pi}{3} \approx \boxed{9.425 \, m^2}$
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