Precalculus (10th Edition)

Published by Pearson
ISBN 10: 0-32197-907-9
ISBN 13: 978-0-32197-907-0

Chapter 6 - Trigonometric Functions - 6.1 Angles and Their Measure - 6.1 Assess Your Understanding: 90

Answer

$s\approx7.854$ centimeters $A\approx35.343$ square centimeters

Work Step by Step

To use the formula for Area of a segment and length of an arc, the angle needs to be in radians. To convert from degrees to radians, the answer in degrees must be multiplied by $\frac{\pi}{180}$. Therefore $50°= 50 \times \frac{\pi}{180}$ $=\frac{5\pi}{18}$ radians $s=r\times\theta$ $s=9\times\frac{5\pi}{18}$ meters Therefore $s\approx7.854$ centimeters $A=\frac{1}{2}\theta r^{2}$, where the angle, $\theta$ measured in radians $A=\frac{1}{2}(\frac{5\pi}{18}) (9)^{2}$ $A\approx 35.343$ square centimeters
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