Precalculus (6th Edition) Blitzer

Published by Pearson
ISBN 10: 0-13446-914-3
ISBN 13: 978-0-13446-914-0

Chapter 4 - Section 4.3 - Right Triangle Trigonometry - Exercise Set: 27

Answer

$\sin{(\frac{\pi}{10})}$

Work Step by Step

RECALL: The cofunction Identities: (1) $\sin{\theta} = \cos{(\frac{\pi}{2}-\theta)}$ (2) $\cos{\theta} = \sin{(\frac{\pi}{2}-\theta)}$ (3) $\tan{\theta} = \cot{(\frac{\pi}{2}-\theta)}$ (4) $\cot{\theta} = \tan{(\frac{\pi}{2}-\theta)}$ (5) $\csc{\theta} = \sec{(\frac{\pi}{2}-\theta)}$ (6) $\sec{\theta} = \csc{(\frac{\pi}{2}-\theta)}$ Use identity (2) to obtain: $\cos{\frac{2\pi}{5}} \\= \sin{(\frac{\pi}{2}-\frac{2\pi}{5})} \\= \sin{(\frac{5\pi}{10}-\frac{4\pi}{10})} \\=\sin{(\frac{\pi}{10})}$
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