Precalculus (6th Edition) Blitzer

Published by Pearson

Chapter 8 - Cumulative Review Exercises - Page 952: 22

Answer

$\frac{3}{5}$

Work Step by Step

Step 1. Let $u=tan^{-1}(-\frac{4}{3})$. We have $tan(u)=-\frac{4}{3}$ and $-\frac{\pi}{2}\lt u\leq 0$ Step 2. Form a right triangle with angle $u$ and sides $4,3,5$, we have $cos(u)=\frac{3}{5}$ Step 3. We have $cos[tan^{-1}(-\frac{4}{3})]=cos(u)=\frac{3}{5}$

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