Precalculus (6th Edition)

Published by Pearson
ISBN 10: 013421742X
ISBN 13: 978-0-13421-742-0

Chapter 6 - The Circular Functions and Their Graphs - 6.1 Radian Measures - 6.1 Exercises: 78

Answer

$\color{blue}{s\approx 8800\text{ km}}$

Work Step by Step

Since they are in opposite directions from the equator, the central angle between the two cities is: $=45^o+34^o=79o$ Convert the angle to radians by multiplying $\dfrac{\pi}{180^o}$ to the angle measure to obtain: $=79 \cdot \dfrac{\pi}{180^o}=\dfrac{79\pi}{180}$ RECALL: The length of the arc $(s)$ intercepted by the central angle $\theta$ in a circle of radius $r$ is given by the formula: $s = r\theta$, where $\theta$ is in radian measure. Use the formula above to obtain: $s=r\theta \\s=6400 \cdot \frac{79\pi}{180} \\s=8824.384698 \\\color{blue}{s\approx 8800\text{ km}}$
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