Chapter 4.4, Problem 4E

To determine

To find $\sec \left(\theta \right)$ .

Answer to Problem 4E

The $\sec \left(\theta \right)=\frac{\sqrt{x^2+y^2}}{x}$ .

Explanation of Solution

Given information:

The angle $\theta$ is in standard position with point $\left(x,y\right)$ on the terminal side of $\theta$ , and $r=\sqrt{x^2+y^2}\ne 0$ .

Calculation:

The angle $\theta$ is in standard position with point $\left(x,y\right)$ on the terminal side of $\theta$ is shown below in the diagram.

  

So, from the above triangle ABC.

  $\begin{array}{c}\sec \left(\theta \right)=\frac{\text{hypotenuse}}{\text{adjacent}}\\ \sec \left(\theta \right)=\frac{r}{x}\end{array}$

Substitute $r=\sqrt{x^2+y^2}$ .

  $\sec \left(\theta \right)=\frac{\sqrt{x^2+y^2}}{x}$ .