Answer
$-\frac{4}{3}$
Work Step by Step
Step 1. Letting $cos^{-1}(\frac{4}{5})=u$, we have $cos(u)=\frac{4}{5}$, thus $cot(u)=\frac{4}{3}$
Step 2. We have $sin^{-1}(1)=\frac{\pi}{2}$
Step 3. $tan(u+\frac{\pi}{2})=-cot(u)=-\frac{4}{3}$
Precalculus (10th Edition)
by Sullivan, Michael
Published by
Pearson
ISBN 10:
0-32197-907-9
ISBN 13:
978-0-32197-907-0
Chapter 7 - Analytic Trigonometry - 7.5 Sum and Difference Formulas - 7.5 Assess Your Understanding - Page 489: 86
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