Definition: Trigonometry is a branch of mathematics that deals with triangles, especially those formed by two rays meeting at a common vertex (a polygon called an angle), as well as how sides of such triangles relate to one another and their respective angles. In this context, "trigonometry" refers to the study of relationships between the sides of triangles. It includes methods used to find trigonometric functions such as sine, cosine, tangent, or inverse trigonometric functions. These are fundamental tools in the study of geometry and can be used to solve problems involving right-angled triangles. The word "trigonometry" is derived from the Greek words 'trig' (meaning "triangle") and 'metron' meaning "measure." The term was introduced in the 16th century by a French mathematician named François Viète, who created a systematic way to calculate trigonometric functions using geometric means. This led to the development of trigonometry as an independent branch of mathematics. Trigonometric functions are based on ratios between sides and angles of triangles. For example, in a right-angled triangle, we know that the side opposite to the angle is the hypotenuse (the longest side), while the other two sides are half of the corresponding sides in a 30-60-90 right triangle, respectively. Trigonometric functions also include inverse trigonometric functions such as sine, cosine, tangent, cotangent, secant and cosecant. In this context, "inverse" means that if we know a particular trigonometric function (for example, sin), we can find the value of its angle by using trigonometric identities. In summary, trigometry is an essential branch of mathematics that deals with the study of triangles to solve problems involving right-angled triangles. It's a fundamental tool in geometry and plays a crucial role in various fields such as physics, astronomy, engineering, and computer graphics.
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