Reference angle

Question

What is a reference angle? Make sure your create an example of using a reference angle as part of your explanation.

Answer 1

Here's a picture

In this case, the angle and the reference angle are the same because the angle is already less than 90°

In this case the angle is greater than 90° so the reference angle is the supplement to it.

Answer 2

A reference angle is the acute angle formed when you plot a given angle on an xy coordinate plane. With the initial side of the angle on the positive x-axis, you rotate counterclockwise for positive angles and clockwise for negative angles.

The other side of the angle, terminal side, will be drawn at the end of the angle rotation. The acute angle formed by the terminal side and the closest part of the x-axis is the reference angle.

In this example, 57° would be the reference angle to 237° (Half a circle rotation is 180°... 237° - 180° = 57°)