Answer
$2\sqrt 2$.
Work Step by Step
1. Let $cos^{-1}\frac{1}{3}=t$, we have $cos(t)=\frac{1}{3}$ and $t$ in quadrant I.
2. Let $x=1, r=3$, we have $y=\sqrt {3^2-1^2}=2\sqrt 2$.
3. Thus $tan(cos^{-1}\frac{1}{3})=tan(t)=\frac{y}{x}=2\sqrt 2$.
Precalculus: Concepts Through Functions, A Unit Circle Approach to Trigonometry (3rd Edition)
by Sullivan III, Michael
Published by
Pearson
ISBN 10:
0-32193-104-1
ISBN 13:
978-0-32193-104-7
Chapter 6 - Analytic Trigonometry - Section 6.2 The Inverse Trigonometric Functions (Continued) - 6.2 Assess Your Understanding - Page 480: 26
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