Algebra and Trigonometry 10th Edition

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

Chapter 6 - Chapter Test - Page 503: 7


$\theta$ lies in the third quadrant.

Work Step by Step

$sec~\theta\lt0$: $\frac{1}{cos~\theta}\lt0$ $cos~\theta\lt0$ $tan~\theta\gt0$ $\frac{sin~\theta}{cos~\theta}\gt0$ Then $sin~\theta\lt0$ because both $sin~\theta$ and $cos~\theta$ must have the same sign. We can conclude that $\theta$ lies in the third quadrant.
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