What defines coterminal angles?

Coterminal angles are angles that share the same initial and terminal sides, meaning that when you position them in standard position (where the initial side is along the positive x-axis), they overlap completely. For example, a 30-degree angle and a 390-degree angle are coterminal because if you were to rotate a 30-degree angle and then another rotation of 390 degrees, they both arrive at the same terminal side in the coordinate plane.

The definition of coterminal angles extends to any angle, such that adding or subtracting full rotations of 360 degrees (or equivalent in radians) will yield coterminal angles. This characteristic clearly sets them apart from other types of angles and helps to identify them, reinforcing the notion that the angles will appear identical in terms of their orientation and placement on a coordinate system.