Trigonometry studies relationships involving lengths and angles of triangles. It emerged from applications of geometry to astronomy during the 3rd century BC. Basic trigonometric identities include tan x sin x + cos x = sec x and cos^2 20+cos^2 70/sin^2 31+sin^2 59+sin^2 64+cos64.sin26 = 2. Applications involve the line of sight from an observer's eye to an airplane overhead, defining the angle of elevation, and the pilot's downward line of sight, defining the angle of depression.