Trigonometry deals with relationships between the sides and angles of triangles, specifically right triangles where one angle is 90 degrees. It originated over 4000 years ago with ancient Egyptian, Mesopotamian, and Indus Valley civilizations, possibly for calculating sundials. Key concepts in trigonometry include the trigonometric functions sine, cosine, and tangent, which relate a triangle's angles to its sides, as well as Pythagoras' theorem for relating sides in a right triangle. Trigonometry has many applications in fields like construction, astronomy, navigation, acoustics, and engineering.