Calculus: Early Transcendentals (2nd Edition)

Published by Pearson
ISBN 10: 0321947347
ISBN 13: 978-0-32194-734-5

Chapter 1 - Functions - Review Exercises - Page 52: 29


$\textbf{a.}$ $\dfrac{3\pi}{4}$ $\textbf{b.}$ $144°$ $\textbf{c.}$ $s=\dfrac{40\pi}{3}\approx41.8879$

Work Step by Step

$\textbf{a.}$ Convert $135°$ to radian measure To convert degrees to radians, multiply the degrees by $\dfrac{\pi}{180°}$ and simplify: $135°\Big(\dfrac{\pi}{180°}\Big)=\dfrac{135\pi}{180}=\dfrac{3\pi}{4}$ $\textbf{b.}$ Convert $4\pi/5$ to degree measure To convert radians to degrees, multiply the radians by $\dfrac{180°}{\pi}$ and simplify: $\Big(\dfrac{4\pi}{5}\Big)\Big(\dfrac{180°}{\pi}\Big)=\dfrac{4(180°)\pi}{5\pi}=\dfrac{720°}{5}=144°$ $\textbf{c.}$ What is the length of the arc on a circle of radius $10$ associated with an angle of $4\pi/3$ (radians)? The formula for the arc length is $s=r\theta$, where $r$ is the radius of the circle and $\theta$ is the angle measured in radians. Both the radius and the angle are known. Substitute them into the formula and evaluate to obtain the arc length: $s=10\Big(\dfrac{4\pi}{3}\Big)=\dfrac{40\pi}{3}\approx41.8879$
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