Chapter 6 - Analytic Trigonometry - Section 6.2 The Inverse Trigonometric Functions (Continued) - 6.2 Assess Your Understanding - Page 480: 45

$1.32$

Let $\theta = \sec^{-1} {4}$ Then, $\sec{\theta} = 4$ Since $\cos{\theta}= \dfrac{1}{\sec{\theta}}$, then $\cos{\theta} = \dfrac{1}{4}$ Thus, $\theta = \cos^{-1} {\left(\frac{1}{4}\right)}\approx 1.32$ Hence, $\sec^{-1} {4} = \cos^{-1} {\left(\frac{1}{4}\right)} \approx \boxed{1.32}$