What is the reference angle?

The reference angle is defined as the smallest positive angle formed by the terminal side of an angle and the x-axis in standard position. It essentially provides a way to describe the location of an angle in relation to the coordinate axes, specifically focusing on its acute version.

When considering the circle's reference, this angle can range between 0 and 90 degrees. For instance, if the angle lies in the first quadrant, it aligns with itself. If it is in the second quadrant, the reference angle is found by subtracting the angle from 180 degrees. If it is in the third quadrant, the reference angle is the angle minus 180 degrees, and in the fourth quadrant, it is 360 degrees minus the angle. This process allows us to standardize angles and make them more manageable, especially when dealing with trigonometric functions.

The other options do not accurately describe what a reference angle is; they pertain to triangle properties rather than the relationship of angles to the x-axis in the Cartesian plane. Thus, focusing on the smallest angle between the terminal side of the angle and the x-axis clearly aligns with the definition of a reference angle.