Precalculus: Concepts Through Functions, A Unit Circle Approach to Trigonometry (3rd Edition)

Published by Pearson
ISBN 10: 0-32193-104-1
ISBN 13: 978-0-32193-104-7

Chapter 5 - Trigonometric Functions - Section 5.3 Properties of the Trigonometric Functions - 5.3 Assess Your Understanding - Page 418: 76


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

Work Step by Step

The cosecant is an odd function so $\csc{(- \theta)} = - \csc{\theta}$ Thus, $\csc{\left(-\dfrac{\pi}{3} \right)} = - \csc{\left(\dfrac{\pi}{3} \right)} =\boxed{-\dfrac{2 \sqrt{3}}{3}}$
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