What angles are used to relate the values returned by inverse trigonometric functions to angles larger than 90 degrees?

For angles between 90 and 180 use the angle (180 - X)

For angles between 180 and 270 use (X - 180)

For angles between 270 and 360 use (360 - X)

For angles greater than 360 subtract 360 until the angle is between 0 and 360 degrees and one of the above rules can be applied.

You need to be careful with the signs of the ratiOS.