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 6 - Analytic Trigonometry - Section 6.2 The Inverse Trigonometric Functions (Continued) - 6.2 Assess Your Understanding - Page 480: 46

Answer

$0.20$

Work Step by Step

Let $\theta = \csc^{-1} {5}$ Then, $\csc{\theta} = 5$. Since $\sin{\theta}= \dfrac{1}{\csc{\theta}}$, then $\sin{\theta} = \dfrac{1}{5}$ Thus, $\theta = \sin^{-1} {\left(\frac{1}{5}\right)}\approx 0.20$ Therefore, $\csc^{-1} {5} = \sin^{-1} {\left(\frac{1}{5}\right)} \approx \boxed{0.20}$
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