Chapter 14.1, Problem 14PPS

To determine

To find:The value of $\tan \theta$

Answer to Problem 14PPS

  $2\sqrt{2}$

Explanation of Solution

Given Information:

We know that, the given expression is $\sec \text{θ}=-3,{180}^{\circ }<\theta <{270}^{\circ }$

Calculation :

  

  $\begin{array}{l}\sec \text{θ}=-\frac{3}{2}=\frac{\text{Hypotenuse}}{\text{Base}}\\ \text{tanθ}=\frac{\text{Perpendicular}}{\text{Base}}\\ \tan \text{θ}=\frac{2\sqrt{2}}{1},{180}^{\circ }<\theta <{270}^{\circ }\end{array}$

In 3rd quadrant $\tan \theta$ is positive.

  $\therefore \boxed{\text{tanθ}=2\sqrt{2}}$