Chapter 12.3, Problem 20WE

To determine

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

Answer to Problem 20WE

  $\alpha =15.8°$

Explanation of Solution

Given:

  $\theta =-344.2°$

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, $\theta =-344.2°$ is negative, first add $360°$ to it to find the counter-clockwise angle $\theta \text{'}=360°-344.2°=15.8°$ ,which is in Quadrant I.

So, the reference angle is :

  $\alpha =\theta \text{'}=15.8°$