Thomas' Calculus 13th Edition

Published by Pearson
ISBN 10: 0-32187-896-5
ISBN 13: 978-0-32187-896-0

Chapter 1: Functions - Section 1.3 - Trigonometric Functions - Exercises 1.3 - Page 27: 9

Answer

$ sin(x)=-\frac{2\sqrt 2}{3}$ and $ tan(x)=-2\sqrt 2$

Work Step by Step

Given $ cos(x)=\frac{1}{3}$ and $ x\in[-\frac{\pi}{2},0]$, we can predict that both $ sin(x)$ and $ tan(x)$ will be negative. The three sides of the right triangle can be chosen as $1,2\sqrt 2, 3$, so $ sin(x)=-\frac{2\sqrt 2}{3}$ and $ tan(x)=-2\sqrt 2$
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