Answer
$-\dfrac{2 \sqrt{3}}{3}$
Work Step by Step
The cosecant is an odd function so
$\csc{(- \theta)} = - \csc{\theta}$
Thus,
$\csc{\left(-\dfrac{\pi}{3} \right)} = - \csc{\left(\dfrac{\pi}{3} \right)} =\boxed{-\dfrac{2 \sqrt{3}}{3}}$
Precalculus: Concepts Through Functions, A Unit Circle Approach to Trigonometry (3rd Edition)
by Sullivan III, Michael
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
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