Calculus with Applications (10th Edition)

Published by Pearson
ISBN 10: 0321749006
ISBN 13: 978-0-32174-900-0

Chapter 13 - The Trigonometric Functions - 13.1 Definitions of the Trigonometric Functions - 13.1 Exercises - Page 678: 34

Answer

$$\frac{{\sqrt 3 }}{2}$$

Work Step by Step

$$\eqalign{ & \cos \frac{\pi }{6} \cr & {\text{convert }}\frac{\pi }{6} {\text{radians to degrees}} \cr & \frac{\pi }{6}{\text{radians}} = \frac{\pi }{6}\left( {\frac{{{{180}^ \circ }}}{\pi }} \right) \cr & \frac{\pi }{6}{\text{radians}} = {30^ \circ } \cr & \cos \frac{\pi }{6} = \cos {30^ \circ } \cr & {\text{using the }}{30^ \circ }{\text{ - 6}}{{\text{0}}^ \circ }{\text{ - 9}}{{\text{0}}^ \circ }{\text{ triangle to obtain}} \cr & \cos {30^ \circ } = \frac{{{\text{adjacent side to the 3}}{{\text{0}}^ \circ }}}{{{\text{hyppotenuse}}}} \cr & \cos {30^ \circ } = \frac{{\sqrt 3 }}{2} \cr & and \cr & \cos \frac{\pi }{6} = \frac{{\sqrt 3 }}{2} \cr} $$
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