Precalculus (10th Edition)

Published by Pearson
ISBN 10: 0-32197-907-9
ISBN 13: 978-0-32197-907-0

Chapter 6 - Trigonometric Functions - 6.3 Properties of the Trigonometric Functions - 6.3 Assess Your Understanding: 26

Answer

$\dfrac {2\sqrt {3}}{3}$

Work Step by Step

$\sec{\alpha} =\sec{\left( \alpha -2\pi n\right)} \\ \Rightarrow \sec{\dfrac {25\pi }{6}}=\sec{\left( \dfrac {25\pi }{6}-4\pi \right)} \\ =\sec{\dfrac {\pi }{6}} \\=\dfrac {1}{\cos \frac {\pi }{6}} \\=\dfrac {1}{\frac {\sqrt {3}}{2}} \\=\dfrac {2\sqrt {3}}{3}$
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