Chapter 7 - Analytic Trigonometry - 7.2 The Inverse Trigonometric Functions (Continued) - 7.2 Assess Your Understanding - Page 458: 26

$2\sqrt 2$

Step 1. Letting $cos^{-1}\frac{1}{3}=t$, we have $cos(t)=\frac{1}{3}$ Step 2. Let $x=1, r=3$, and $y=\sqrt {r^2-x^2}=2\sqrt 2$. Step 3. Sides $x,y,r$ form a right triangle with angle $t$ facing $y$. Step 4. We have $tan(t)=\frac{y}{x}=2\sqrt 2$ or $tan(cos^{-1}\frac{1}{3})=2\sqrt 2$