tangent, in mathematics. 1 In geometry, the tangent to a circle or sphere is a straight line that intersects the circle or sphere in one and only one point. For other curves and surfaces the tangent line at a given point P is defined as the limiting position, if such a limit exists, of a secant line through P and another point P′ on the curve or surface as P′ is allowed to approach P. The tangent plane to a surface at a point is the plane in which every line in the plane that passes through the point is a tangent line to the surface at that point. The study of tangent lines and planes usually requires the concepts of the calculus and is included within the scope of differential geometry. 2 A trigonometric function. See trigonometry.