Winkelwerte

Winkelwerte, or angle values, are numerical measures of the size of an angle, typically expressed in degrees or radians. An angle is the measure of rotation from one ray to another that share a common endpoint. The angle value can be described as the smaller, interior angle in non-oriented contexts, or as an oriented angle that reflects direction and may exceed the usual ranges.

Common ranges: for non-oriented angles, 0 to 180 degrees (0 to π radians). Oriented angles can be negative or exceed 180 degrees and are often considered modulo 360 degrees (2π radians) to yield a principal value.

In geometry and trigonometry, Winkelwerte describe polygon interior angles, the angle between lines or vectors, and the arguments of trigonometric functions. The angle between two vectors u and v is defined via arccos((u·v)/(|u||v|)); orientation can be determined with the sign of a cross product or by atan2.

Sum rules: in Euclidean polygons, the sum of interior angle values is (n−2)×180 degrees for an n‑sided polygon; triangles therefore sum to 180 degrees. Conversions: 1 circle equals 360 degrees or 2π radians; to convert degrees to radians multiply by π/180, and radians to degrees multiply by 180/π.

Applications include computer graphics for rotations, surveying and navigation for bearings, and physics for angular measurements. See also: angle, degree, radian, arccos, atan2.