Chapter 4.4, Problem 104E

To determine

if the given statement is true.

Answer to Problem 104E

False

Explanation of Solution

Given:

The statement, “The reference angle for an angle $\theta$ (in degrees) is the angle ${\theta }^{\prime }=360°n-\theta$ , where n is an integer and $0°\le \theta \le 360°$.”

The given statement is false.

The reference angle of an angle $\theta$ is the acute angle ${\theta }^{\prime }$ formed by the terminal side of $\theta$ and the horizontal axis.

Reference angle ${\theta }^{\prime }$ depends on the quadrant in which the angle $\theta$ lies.

If $\theta$ lies in 2^nd quadrant, reference angle is ${\theta }^{\prime }=180°-\theta$ .

If $\theta$ lies in 3^rd quadrant, reference angle is ${\theta }^{\prime }=\theta -180°$ .

If $\theta$ lies in 4^th quadrant, reference angle is ${\theta }^{\prime }=360°-\theta$ .