Chapter 6 - Inverse Circular Functions and Trigonometric Equations - Section 6.4 Equations Involving Inverse Trigonometric Functions - 6.4 Exercises - Page 280: 27

$x=-2{\sqrt 2}$

Given: $\frac{4}{3}cos^{-1}\frac{x}{4}=\pi$ $\frac{4}{3}cos^{-1}\frac{x}{4}=\frac{3 \pi}{4}$ $\frac{x}{4}=cos(\frac{3 \pi}{4})$ $x=4cos(\frac{3 \pi}{4})$ (Multiply by 4) Apply definition of arccosine. $x=-4(\frac{\sqrt 2}{2})$ Hence, $x=-2{\sqrt 2}$