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 388: 120

Answer

$44-4\pi$ square units

Work Step by Step

$AE=AB=r=\frac{s}{\theta}=\frac{2\pi}{\pi/2}=4$ Area of the rectangle=$AB\times AD=4(7+4)=44$ Area of the sector=$\frac{1}{2}r^{2}\theta=\frac{1}{2}\times(4)^{2}\times\frac{\pi}{2}=4\pi$ $\text{Area of the portion outside the circle= Area of the rectangle- Area of the sector}$ $=44-4\pi$ square units
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