Answer
$-\frac{\pi}{2}$.
Work Step by Step
Vertical asymptotes of the graph $y=tan(x)$ can be written as $x=n\pi+\frac{\pi}{2}$ where $n$ is an integer. Thus the greatest negative value is $k=-\frac{\pi}{2}$.
Precalculus (6th Edition)
by Lial, Margaret L.; Hornsby, John; Schneider, David I.; Daniels, Callie
Published by
Pearson
ISBN 10:
013421742X
ISBN 13:
978-0-13421-742-0
Chapter 6 - The Circular Functions and Their Graphs - 6.5 Graphs of the Tangent and Cotangent Functions - 6.5 Exercises - Page 623: 5
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