Chapter 13.1, Problem 20PPS

To determine

To find: The value of $\text{cosθ}$

Answer to Problem 20PPS

  $\frac{4}{5}$

Explanation of Solution

Given Information:

We know that, the given expression is $\text{cosecθ}=\frac{-5}{3},{270}^{\circ }<\theta <{360}^{\circ }$

Calculation :

  $\begin{array}{l}\text{cosecθ}=\frac{-5}{3}=\frac{\text{Hypotenuse}}{\text{Perpendicular}}\\ \text{cosθ}=\frac{\text{Base}}{\text{Hypotenuse}}\\ \text{cosθ}=\frac{4}{5}\\ \because {270}^{\circ }<\theta <{360}^{\circ }\\ \text{in}{\text{4}}^{\text{th}}\text{quadrant}\text{cosθ}\text{will be positive,}\\ \therefore \text{cosθ}=\frac{4}{5}\end{array}$