Coterminal angles are angles in coordinate plane that result out of rotation of the terminal side of angles in standard position. The angle in standard position has the vertex at the origin and one ray on the positive x -axis, which is called the initial side of the angle. The other ray is called the terminal side of the angle.
In the above example angle measure 45º has initial side on the x-axis and the terminal side along OP. If you imagine OP to be a circling ray, it comes back to the same position after completing one full rotation about the origin. Thus it has described an angle measure of 405º. Angles 45 and 405º both share the terminal ray along OP. If the rotation of OP is continued, it describes angles 765º, 1125º ..... after completing each rotation. All these angle measures are Coterminal angles.
The Coterminal angles makes it possible for the angle to have any real number as its measure and map all these measures to Unit circle angles.
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