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: 47

Answer

$\color{blue}{\approx 2.429 \text{ radians}}$

Work Step by Step

RECALL: (1) $1^0=60'$ (2) To convert an angle in degrees to radians, multiply $\dfrac{\pi}{180^o}$ then simplify. Convert $10'$ to degrees to obtain: $10' = 10' \cdot \dfrac{1^o}{60'} = \dfrac{1}{6}^o$ Thus, the given measurement is equivalent to: $139\frac{1}{6}^o$ Convert to radians using the formula in (2) above to obtain: $\require{cancel} 139\frac{1}{6}^o \\= 139\frac{1}{6}^o \cdot \dfrac{\pi}{180^o} \\=2.428916542 \text { radians} \\\color{blue}{\approx 2.429 \text{ radians}}$
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