Determining reference angles.

First, if it falls in quadrant one...

... the reference angle is the angle you were initially given. By the way, we'll call that angle THETA from now on for this description.

How do you determine reference angles you ask?

First, determine the quadrant the terminal side falls into.

What is the appropriate subtraction?

It depends on the quadrant the angle terminates in.

After you determine the quadrant the terminal side falls into...

Use the appropriate subtraction, if necessary, to determine the reference angle.

If it falls into quadrant three?

we do the opposite of the previous instruction, we subtract 180 degrees from THETA.

And lastly, if it falls into quadrant four

we subtract THETA from 360 degrees (the value of the x axis that is closer to the angle)

Second, if it falls in quadrant two

we subtract the THETA angle from 180 degrees (the value of the x axis that is closer to the angle)