Trigonometry is the branch of mathematics that deals with the relationships between angles and sides of triangles. It focuses on the mathematical properties of right-angled triangles. Trigonometry is used in many different fields, including engineering, architecture, physics, and astronomy.

The most basic concepts in trigonometry are the three primary ratios: sine (sin), cosine (cos), and tangent (tan). These ratios are used to calculate the angle measures within a triangle based on its side lengths. The sin ratio is defined as the ratio of the length of the side opposite an angle to the length of the hypotenuse; cosine is the ratio of the adjacent leg to the hypotenuse, and tangent is the ratio opposite leg to the adjacent leg.

There are also several secondary ratios and identities that can be derived from these primary ratios. These include things like cosecant (csc), secant (sec), cotangent (cot), and so on. These secondary ratios are particularly useful for solving problems involving more complex shapes than just a simple right-angled triangle.