Precalculus (10th Edition)

Published by Pearson
ISBN 10: 0-32197-907-9
ISBN 13: 978-0-32197-907-0

Chapter 7 - Analytic Trigonometry - 7.2 The Inverse Trigonometric Functions (Continued) - 7.2 Assess Your Understanding - Page 458: 45

Answer

$1.32$

Work Step by Step

Note that $\sec {x}=\frac{1}{\cos{(x)}}$. Hence, $\sec^{-1}{x}=\cos^{-1} {\left(\frac{1}{x}\right)}$. Use a calculator in radian mode, use its inverse cosine function and round the result to two decimal places to obtain: $\sec^{-1}{(4)}=\cos^{-1} {\left(\frac{1}{4}\right)}\approx1.32$
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