Trigonometry studies the relationships between sides and angles of triangles, with origins in Ancient Egypt and formalization by the Greeks. It includes six major functions and identities, and is used in fields such as engineering, surveying, and astronomy for real-life applications.
Trigonometry is a specialized branch of geometry that deals with the study of triangles. It is sometimes informally referred to as a “trig”. In trigonometry, mathematicians study the relationships between the sides and angles of triangles. Right triangles, which are triangles at a 90-degree angle, are a key area of study in this area of mathematics.
It is commonly believed that the word trigonometry comes from the Greek words trigonon and metron meaning “triangle” and “measure” respectively. This is a very ancient science that may have been used in a basic form in Ancient Egypt. It was the Greeks who formalized the first trigonometric functions, starting with Hipparchus of Bithynia around 150 BC
Trigonometric functions describe the relationships between the angles and sides of a triangle. In modern mathematics, there are six major trigonometric functions, also called trigonometric formulas: sine, tangent, secant, cosine, cotangent, and cosecant. These functions describe the ratios of the sides of right triangles.
Trigonometric identities are algebraic equations that are important elements of the study of triangles. Trigonometric identities include Pythagorean identities, reduction formulas, and cofunction identities. Often, a trigonometry calculator is used to solve trigonometry problems.
Trigonometry courses may cover study topics such as how to use trigonometric functions to solve right triangles and the Pythagorean theorem. Also, non-rectangular triangles can be solved using the sine and cosine trigonometric functions. More advanced educational courses may include the study of complex numbers, polar coordinates, De Moivre’s theorem and Euler’s formula.
The real-life applications of this branch of mathematics are many and varied. Engineers in many industrial fields use the trig in the course of their work. Other professionals who may use trigonometry include surveyors, astronomers, architects and pilots.
A common real-life problem that can be solved using the rules of trigonometry is working out the measurements of things or spaces that would be difficult to measure directly in the traditional way. For example, trigonometric functions can be used to calculate the height of mountains, the amount of water in a lake, or the square footage of an unusually shaped piece of land. Trigonometry can also be used to help astronomers measure time accurately.
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