Answer
$-\frac{4}{3}$
Work Step by Step
1. Let $cos^{-1}(\frac{4}{5})=u$ (quadrant I), we have $cos(u)=\frac{4}{5}, cot(u)=\frac{4}{3}$
2. Let $sin^{-1}(1)=v$, we have $v=\frac{\pi}{2}$
3. Thus $tan(u+v)=tan(u+\frac{\pi}{2})=-cot(u)=-\frac{4}{3}$
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 6.5 Sum and Difference Formulas - 6.5 Assess Your Understanding - Page 509: 84
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