Algebra and Trigonometry 10th Edition

Published by Cengage Learning
ISBN 10: 9781337271172
ISBN 13: 978-1-33727-117-2

Chapter 6 - 6.6 - Inverse Trigonometric Functions - 6.6 Exercises - Page 485: 57



Work Step by Step

Let $u=arctan(-\frac{3}{5})$. Then: $tan~u=-\frac{3}{5}$ The range $arctan~x$ is $-\frac{\pi}{2}\lt x\lt\frac{\pi}{2}$. So, since $arctan(-\frac{3}{5})\lt0$, then $-\frac{\pi}{2}\lt u\lt0~~$ (Fourth Quadrant) $cot[arctan(-\frac{3}{5})]=cot~u=\frac{1}{tan~u}=-\frac{5}{3}$
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