Trigonometry (10th Edition)

Published by Pearson
ISBN 10: 0321671775
ISBN 13: 978-0-32167-177-6

Chapter 3 - Radian Measure and the Unit Circle - Section 3.2 Applications of Radian Measure - 3.2 Exercises - Page 105: 38


$4\pi$ inches

Work Step by Step

Step 1: The formula to be used here is $s=r\theta$ where $s$ is the length of the arc intercepted on a circle of radius $r$ by a central angle of measure $\theta$ radians. Step 2: In this case, $r=3$ inches. Step 3: $60$ minutes= $2\pi$ radians $40$ minutes= $x$ radians Using ratios and cross multiplication: $\frac{60}{2\pi}=\frac{40}{x}$ $60x=80\pi$ $x=\frac{80\pi}{60}=\frac{4\pi}{3}$ Therefore, $40$ minutes represents $\frac{4\pi}{3}$ radians. Step 4: The distance traveled by the tip of the minute hand is represented by the arc length $s$. Step 5: Therefore $s=r\theta=(3)(\frac{4\pi}{3})=4\pi$ inches
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