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 - Chapter Review - Review Exercises - Page 459: 49


$\dfrac{\pi}{3}=1.0472 \approx1.047 \ ft $ and $\dfrac{\pi}{3} \approx1.047 \ ft^2$

Work Step by Step

The arc length is given by: $=(r) (\dfrac{\theta}{180}) ( \pi)=(2) \cdot (\dfrac{30}{180}) \cdot \pi=\dfrac{\pi}{3}=1.0472 \approx1.047 \ ft $ The area of a sector is given by: $A=\dfrac{\theta}{360}\cdot \pi \cdot r^2$ ( $\theta$ is in degrees) Now, $A=\dfrac{30}{360}\cdot \pi \cdot 2^2=\dfrac{120 \pi }{360} =\dfrac{\pi}{3} \approx1.047 \ ft^2$
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