## Algebra and Trigonometry 10th Edition

$\theta$ lies in the third quadrant.
$sec~\theta\lt0$: $\frac{1}{cos~\theta}\lt0$ $cos~\theta\lt0$ $tan~\theta\gt0$ $\frac{sin~\theta}{cos~\theta}\gt0$ 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.