## Precalculus (6th Edition)

Published by Pearson

# Chapter 6 - The Circular Functions and Their Graphs - 6.1 Radian Measures - 6.1 Exercises - Page 573: 51

#### Answer

$\color{blue}{\approx 0.3134 \text{ radians}}$

#### 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 $25'$ to degrees to obtain: $25' = 25' \cdot \dfrac{1^o}{60'} = \dfrac{5}{12}^o$ Thus, the given measurement is equivalent to $56\frac{5}{12}^o$ Convert to radians using the formula in (2) above to obtain: $\require{cancel} 56\frac{5}{12}^o \\= 56\frac{5}{12}^o \cdot \dfrac{\pi}{180^o} \\=0.3134259259 \\\color{blue}{\approx 0.3134 \text{ radians}}$

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