Trigonometry deals with relationships between sides and angles of triangles. It uses basic formulas relating opposite, adjacent, and hypotenuse sides to trigonometric functions of an angle. These formulas apply to right triangles and can be extended to any angle using concepts like reference angles, coterminal angles, radians, and the unit circle. Mastering basic trigonometric functions, special angle values, and identities provides the foundation for applying trigonometry to solve problems.