Nullwinkel

Nullwinkel, literally "zero angle" in German, is the angle measure equal to 0 degrees between two rays or lines in a plane. It signifies that the directions coincide and serves as a baseline or reference direction in angular measurements. In standard geometry and trigonometry, angles are typically measured from a chosen reference axis; the nullwinkel corresponds to θ = 0, and the orientation remains unchanged by any further rotation.

In a two-dimensional coordinate system, an angle of zero places the reference along the positive x-axis. Points described in polar coordinates with θ = 0 lie on this axis. In the unit circle, the point (1, 0) corresponds to the null angle, with cos(0) = 1 and sin(0) = 0. In the context of rotations, a rotation by the null angle is the identity transformation.

The term is common in German-language mathematical literature and is used to describe the baseline when defining angular measurements, including the use of protractors or angular coordinate systems. The nullwinkel is distinct from other special angles, such as the right angle (90°) or obtuse angles (>90°). It is also related to zero in trigonometric functions, representing the starting value in various parameterizations and series expansions involving angles.