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: 54



Work Step by Step

Let $\theta = \sec^{-1} {\left(-\frac{4}{3}\right)}$ Then, $\sec{\theta} = -\dfrac{4}{3}$. Since $\cos{\theta}= \dfrac{1}{\sec{\theta}}$, then $\cos{\theta} = \dfrac{1}{-\frac{4}{3}}=-\dfrac{3}{4}$ Thus, $\theta = \cos^{-1} {\left(-\frac{3}{4}\right)}\approx 2.42$ Hence, $\sec^{-1} {\left(-\frac{4}{3}\right)}= \cos^{-1} {\left(-\frac{3}{4}\right)} \approx \boxed{2.42}$
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