Chapter 7 - Analytic Trigonometry - 7.2 The Inverse Trigonometric Functions (Continued) - 7.2 Assess Your Understanding - Page 458: 54

$2.42$

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 and round the result to decimal places to obtain $\sec^{-1}{(-\frac{4}{3})}=\cos^{-1} {\left(\dfrac{1}{-\frac{4}{3}}\right)}\approx2.42$