Chapter 12.3, Problem 11WE

To determine

For angle $\theta$ , find its quadrant and its refrence angle.

Answer to Problem 11WE

  $\alpha =25°$

Explanation of Solution

Given:

  $\theta =-205°$

Formula Used:

If $\theta$ is not a quadrantal angle, there is a unique acute angle $\alpha$ corresponding to $\theta$ , formed by the terminal side of $\theta$ and the positive or negative x- axis.When $\theta$ is in standard position , $\alpha$ is called the reference angle of $\theta$ .

Calculation:

Since, $\theta =-205°$ is negative , first add $360°$ to make it positive $\theta \text{'}=360°-205°=155°$ , which is in Quadrant II.

So, the reference angle is :

  $\alpha =180°-\theta \text{'}=180°-155°=25°$