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 - Page 575: 82

Answer

$213^\circ$

Work Step by Step

1. We know that the two gears should travel the same arc length. 2. For the smaller gear, we have the arc length traveled as $L_1=4.8\times315^\circ\times\frac{\pi}{180^\circ}\ in$ 3. For the larger gear, we have the arc length traveled as $L_2=7.1\times \theta^\circ\times\frac{\pi}{180^\circ}\ in$ 4. Let $L_2=L1$, we can find $\theta=\frac{4.8\times315}{7.1}\approx213^\circ$
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