Chapter 12.3, Problem 9WE

To determine

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

Answer to Problem 9WE

  $\alpha =53°$

Explanation of Solution

Given:

  $\theta =233°$

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 $180°<\theta =233°<270°$ , the angle is in Quadrant III.So, the reference angle is :

  $\alpha =\theta -180°=233°-180°=53°$