## Calculus 8th Edition

Published by Cengage

# Appendix D - Trigonometry - D Exercises: 27

#### Answer

$sin\frac{5\pi}{6}=\frac{1}{2}$ $cos\frac{5\pi}{6}=-\frac{\sqrt 3}{2}$ $tan\frac{5\pi}{6}=-\frac{\sqrt 3}{3}$ $csc\frac{5\pi}{6}=2$ $sec\frac{5\pi}{6}=-\frac{2\sqrt 3}{ 3}$ $cot\frac{5\pi}{6}=-\sqrt 3$

#### Work Step by Step

Since, $\frac{5\pi}{6}$ lies on second quadrant, thus its reference angle will be $\pi-\frac{5\pi}{6}=\frac{\pi}{6}$, which can be considered as common angle to all trigonometric ratios. The trigonometric ratios and their inverse trigonometric ratios are given as follows: $sin\frac{5\pi}{6}=sin\frac{\pi}{6}=\frac{1}{2}$ $cos\frac{5\pi}{6}=-cos\frac{\pi}{6}=-\frac{\sqrt 3}{2}$ $tan\frac{5\pi}{6}=-tan\frac{\pi}{6}=-\frac{\sqrt 3}{3}$ $csc\frac{5\pi}{6}=\frac{1}{sin\frac{5\pi}{6}}=2$ $sec\frac{5\pi}{6}=\frac{1}{cos\frac{5\pi}{6}}=-\frac{2\sqrt 3}{ 3}$ $cot\frac{5\pi}{6}=\frac{1}{tan\frac{5\pi}{6}}=-\sqrt 3$

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