Chapter 12.3, Problem 1OE

To determine

State the measure of the reference angle $\alpha$ for each angle $\theta$ .

Answer to Problem 1OE

  $\alpha =45°$

Explanation of Solution

Given:

  

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 the angle is in 2^nd quadrant , the reference angle is

  $\alpha =180°-\theta =180°-135°=45°$