Trigonometry 7th Edition

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

Chapter 2 - Section 2.2 - Calculators and Trigonometric Functions of an Acute Angle - 2.2 Problem Set - Page 73: 96

Answer

III quadrant.

Work Step by Step

We know that $\tan\theta=\frac{y}{x}$ and $\sec \theta=\frac{1}{\cos \theta}=\dfrac{R}{x}.$ Where $R$ is always $R>0$. If $\tan\theta > 0$ then ($y>0$ and $x>0$) or ($y<0$ and $x<0$). It's true for I quadrant and III quadrant. if $\sec \theta <0$ then $x<0.$ It's true for II and III quadrants. Both conditions are true only for III quadrant.
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