Trigonometry 7th Edition

Published by Cengage Learning
ISBN 10: 1111826854
ISBN 13: 978-1-11182-685-7

Chapter 1 - Section 1.3 - Definition I: Trigonometric Functions - 1.3 Problem Set - Page 32: 54

Answer

$QI$ (both positive), $QII$ (both negative).

Work Step by Step

$\cos{\theta} = \dfrac{x}{r} \hspace{10pt } \& \hspace{10pt} \cot{\theta} = \dfrac{x}{y}$ $r = \sqrt{x^2+y^2} \hspace{10pt} \therefore$ $r$ is always positive. $y$ is positive in $QI$ and $QII$ $\therefore \cos{\theta}$ and $\cot{\theta}$ have the same sign in $QI$ and $QII$ $\because x$ is positive in $QI$ $\hspace{36pt}$ $\therefore \cos{\theta}$ and $\cot{\theta}$ are positive in $QI$ $\because x$ is negative in $QII$ $\hspace{30pt}$ $\therefore \cos{\theta}$ and $\cot{\theta}$ are negative in $QII$
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