Trigonometry studies relationships between angles, heights, and lengths of triangles. Applications include astronomy, engineering, architectural design, and physics. Trigonometric identities help solve problems better through formulas
Menelaus of Alexandria (98AD) proved that if three points are collinear, then AZ.BX.CY = 1. The theorem can be proved using area or ratio theorem methods. The converse of Menelaus' theorem states that if AZ.BX.CY = 1, then X, Y, Z are collinear
Cos2x is a trigonometric function for calculating cosine for angle 2x. The formula is cos2x = cos²x - sin²x. Cosine is the ratio of side nearest to angle to hypotenuse in triangle
Barycentric coordinates specify points relative to a simplex (triangle or tetrahedron). Points have barycentric coordinates that sum to zero. Two tuples of barycentric coordinates specify same point if proportional. System was introduced by August Möbius in 1827