Each rotation of OM corresponds to a certain angle.


Zero angle of rotation


If OM coincides with OK, then this arrangement of rays corresponds to the zero angle. In trigonometry, such a mutual arrangement of rays is called the initial position.

Нулевой угол поворота

Zero angle of rotation

Round angle of rotation


This is a “full rotation” (rot) or “revolution” (rev) or “complete turn” or “full circle“.

If terminal side OM completes such a circle and afterwards coincides with OK, this is called a full circle (turn), which corresponds to an angle of 360° or 2π rad in the positive direction, and −360° (or −2π rad in the negative direction).

1 full circle = 1 rev = 1 turn = 1 rot = 360°

угол поворота

Positive full circle (Positive round angle). Revolution

Right angle


If OM completes one fourth of a full circle, it results in a right angle (positive = 90° or negative = –90° depending on the direction of rotation).

угол поворота

Positive right angle

Straight Angle (Flat angle)


If terminal side OM completes half a full circle, the result is a straight angle (or a flat angle).
If OM rotates counterclockwise, it forms a positive straight angle of 180°.
If OM rotates clockwise, it forms a negative straight angle of –180°.

угол поворота

Positive straight angle

Inverse right angle


 If OM completes three fourths of a full circle (a three quarter rotation), it results in an inverse right angle (positive =270° or negative =–270° depending on the direction of rotation).

Тройной прямой угол

Positive three quarter rotation (Positive inverse right angle)

The general concept of revolutions (turns)

A full circle is 360°:
1 full circle = 1 rev = 1 turn = 1 rot = 360°

A half turn is 180°:
1/2 rev =1/2∙360°= 180°

A quarter turn is 90°:
1/4 rev =1/4∙360°= 90°

An eighth turn is 45°:
1/8 rev=1/8∙360°= 45°

Two revolutions:

2∙360°= 720°

One and a half revolutions:

360°+1/2∙360°= 540°