Chapter 12.3, Problem 15WE

To determine

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

Answer to Problem 15WE

  $\alpha =5°$

Explanation of Solution

Given:

  $\theta =-725°$

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, $\theta =-725°$ which is negative .Add it to three times of $360°$ to find the counter-clockwise angle :

  $\theta \text{'}=1080°-725°=355°$ , which is in Quadrant IV.

So, the reference angle is :

  $\alpha =360°-\theta \text{'}=360°-355°=5°$