Halvvejsvinklen

Halvvejsvinklen is a Danish mathematical term that can denote either the half-angle of a given angle or, more commonly, the line or concept used to bisect that angle. The wording combines halvvejs ("halfway") and vinklen ("the angle"), reflecting its general sense as a division of an angle into two equal parts. In standard Danish mathematical terminology, the more formal phrases are vinkelhalveringslinje for the angle bisector and halvvinkel for half-angle, but halvvejsvinklen may appear in informal or historical texts.

As a geometric concept, an angle bisector is a ray from the vertex of an angle that splits it into two congruent angles. In a triangle, the internal angle bisector divides the opposite side into segments proportional to the adjacent sides (Angle Bisector Theorem).

In trigonometry, the half-angle formulas express trigonometric functions of half of a given angle: sin(x/2) = ±√((1 − cos x)/2), cos(x/2) = ±√((1 + cos x)/2), tan(x/2) = sin x / (1 + cos x) = (1 − cos x)/sin x, with the sign determined by the angle's quadrant.

Uses include geometric constructions, triangle solving, and simplifying integrals or trigonometric expressions. The term serves as a linguistic cue rather than a distinct mathematical object beyond these well-established ideas.

See also: angle, angle bisector, half-angle.