Trigonometry (Complete)

Trigonometry is a branch of mathematics that deals with the study of triangles and the relationships between their sides and angles. It explores the properties of triangles, particularly right triangles, and the trigonometric functions that describe these relationships.

Key concepts in trigonometry include:

1. Trigonometric Ratios: Trigonometric ratios, such as sine (sin), cosine (cos), tangent (tan), cosecant (csc), secant (sec), and cotangent (cot), relate the angles of a triangle to the lengths of its sides. These ratios are defined based on the ratios of the sides of a right triangle.

2. Right Triangle Trigonometry: In right triangle trigonometry, the three primary trigonometric ratios (sine, cosine, and tangent) are used to relate the angles of a right triangle to the lengths of its sides. The Pythagorean theorem and other trigonometric identities are also commonly used in this context.

3. Trigonometric Functions: Trigonometric functions extend the concepts of trigonometric ratios to all angles, not just those in right triangles. These functions are defined for all real numbers and can be represented graphically as periodic functions.

4. Trigonometric Identities: Trigonometric identities are equations that relate the values of trigonometric functions to each other. They are used to simplify trigonometric expressions, prove mathematical statements, and solve trigonometric equations.

Trigonometry has wide-ranging applications in various fields, including physics, engineering, astronomy, navigation, architecture, and computer graphics. It provides tools for analyzing and solving problems involving angles, distances, velocities, forces, and periodic phenomena. Understanding trigonometry is essential for students pursuing careers in STEM (science, technology, engineering, and mathematics) fields and for solving practical problems in real-world scenarios.