In planar geometry on an oriented coordinate plane, there is the concept of coterminal angles, which have a common stationary side and one common movable side. In general, coterminal angles can be called pairs of angles in which one is greater or less than the other by a number divisible by 2pi. That is why there is no exact number of coterminal angles, nor is there a specific direction. In particular, for an angle of 50°, we can continually create at least one positive and one negative coterminal angle. By definition, if the initially given angle was 50°, then the coterminal positive angle is 410°. At the same time, the nearest negative coterminal angle is -310°. Geometrically, these angles were formed by rotating the initial angle a complete turn (or a multiple of a number of turns) in a given direction.
In the terminology of coterminal angles, there is the concept of a terminal and an initial side. The initial side is usually the zero coordinate (horizontal axis) from which the initial angle is counted. If the initial angle was indeed 50°, then it is from the initial side these degrees are counted to conditionally form an acute angle triangle, in which 50° are in the center of the coordinates. The terminal side for the initial angle and the coterminal angle are the same because, as mentioned, the coterminal angle is formed only by rotating a multiple of a whole number of revolutions. Consequently, if the terminal side of the coterminal angle is not the same as the terminal side of the initial angle, then there is a clear error in the definition.
As a first example, we can use an angle A equal to 50°. The nearest positive coterminal angle for A is, as has been shown, 410°. The terminal sides of both angles, in this case, are in the first quarter of the circle. As a second example, we can use angle B equal to 
. There are two ways to do this: either convert the angle from radians to degrees or use only radians. In the first case, the angle can be translated:
Then the nearest positive coterminal angle is 560°, which, like angle B, has a terminal side in quarter III. If the calculation were done in radians, then:
which is also located in the same third quarter.