Precalculus (6th Edition)

Published by Pearson
ISBN 10: 013421742X
ISBN 13: 978-0-13421-742-0

Chapter 7 - Trigonometric Identities and Equations - Chapter 7 Test Prep - Review Exercises - Page 736: 13


$\Rightarrow \sin x=-\dfrac {4}{5}$ $\tan x=-\dfrac {4}{3}$ $\cot \left( -x\right) =\dfrac {3}{4}$

Work Step by Step

In quadrant 4 only cosine function is positive $sine$ $tan$ and $\cot$ are negative $\Rightarrow \sin x=-\sqrt {1-\cos ^{2}\theta }=-\sqrt {1-(\dfrac {3}{5})^{2}}=-\dfrac {4}{5}$ $\tan x=\dfrac {\sin x}{\cos x}=\dfrac {-\dfrac {4}{5}}{\dfrac {3}{5}}=-\dfrac {4}{3}$ $\cot \left( -x\right) =-\cot \left( x\right) =-\dfrac {1}{\tan x}=-\dfrac {1}{-\dfrac {4}{3}}=\dfrac {3}{4}$
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