Trigonometric functions are mathematical relationships that connect the angles of a triangle with the ratios of its sides. The most common ones are sine, cosine, and tangent, which are defined using right triangles. For example, sine measures the ratio of the side opposite an angle to the hypotenuse, while cosine measures the ratio of the adjacent side to the hypotenuse. These functions are not limited to triangles; they are used to describe patterns of waves, oscillations, and circular motion.