CosB

CosB denotes the cosine of angle B, typically in triangle geometry. In triangle ABC, B is the vertex at which the angle is measured, with sides adjacent to B labeled AB and BC and the side opposite B labeled b. Using the standard notation where side a is opposite A, b opposite B, and c opposite C, the Law of Cosines gives b^2 = a^2 + c^2 − 2ac cos B. Therefore cos B = (a^2 + c^2 − b^2) / (2ac). The value of cos B depends only on the angle B and not on the overall size of the triangle, and for a nondegenerate triangle its value lies strictly between −1 and 1.

In a right triangle, if B is one of the non-right angles, cos B equals the ratio of the length of the adjacent leg to the hypotenuse. In vector form, if BA and BC are the vectors from B to A and from B to C, then cos B = (BA · BC) / (|BA||BC|).

CosB is a basic building block in solving triangles, trigonometric identities, and coordinate geometry. It also plays a role in applications across physics and engineering, where the angle B is defined by the geometric configuration under study. The concept remains the same regardless of whether B is considered in a planar triangle, a polygon, or a more general geometric context.