Trigonometry is one of the branches of mathematics that has innumerable applications in real life. Starting from the creation of maps to the calculation of the altitude of tides and waves of seas and oceans, **trigonometry formulas** are used in many areas. Satellite systems take the help of trigonometry as well. It is even used during the investigation process of many crime scenes.

## Broad List of Various Types of Trigonometric Formulas

The trigonometric formulas can be categorized into various types. We will now learn about the various types of trigonometric formulas.

- Basic Trigonometric Ratios Formula: These formulas derive from various trigonometric ratios. These are sine, cosine, tangent, secant, cosecant, and cotangent. Examples of the basic trigonometric ratios formula are discussed below:

sin x = Perpendicular/ Height

cos x = Base/ Height

tan x = Perpendicular/ Base

Other trigonometric ratio formulas can be derived with the help of the ratios mentioned above.

- Trigonometry Formula for Standard Angles: For standard angles such as 0 degree, 30 degree, 45 degree, 60 degree, etc trigonometric values are depicted in a table called the trigonometry ratio formula. Examples of some values of standard angles of trigonometry ratios are discussed below:

sin 0 degree = 0

sin 30 degree = 1/2

sin 45 degree = 1/√2

sin 60 degree = √3/2

sin 90 degree = 1

cos 0 degree = 1

cos 30 degree = √3/2

cos 45 degree = 1/√2

cos 60 degree = 1/2

cos 90 degree = 0

Other trigonometric values of standard angles can be obtained with the help of the values of trigonometry ratios given above.

- Basic Trigonometric (Pythagorean) Identities: These formulas are derived with the help of the Pythagorean theorem which says that the square of the hypotenuse of a right-angled triangle is equal to the sum of the squares of its base and its height. The basic trigonometric identities are:

sin2y + cos2y = 1

1 + tan2y = sec2y

1 + cot2y = cosec2y

- Trigonometric formulas for Cofunction Identities: The trigonometry formulas for cofunction identities deal with the relationship between different trigonometric functions. Some examples of trigonometric formulas for cofunction identities are given below:

cos y = sin(90 degree – y)

sin y = cos(90 degree – y)

cot y = tan(90 degree – y)

tan y =cot(90 degree – y)

## History of the Origin of Trigonometry

One of the earliest studies of the subject of trigonometry can be found in Egyptian mathematics and Babylonian mathematics. In the context of the development of trigonometry in India, it flourished during the period of the Gupta Empire under the leadership of the great mathematician and astronomer, Aryabhatta, who developed the sine function. **Trigonometry** was an independent subject in the Islamic world because they knew all six trigonometric functions. Modern trigonometry developed during the Age of Enlightenment and reached its modern format during the 1750s. In the 18th century, trigonometry further developed when Leonhard Euler established the analytic treatment of various trigonometric functions.

## Trigonometry and Its Origin

Trigonometry is one of the subsets of mathematics that deals with the functioning of the sides and angles of a right-angled triangle. It can be categorized broadly into two types namely, spherical trigonometry and plane trigonometry. Students find this topic very tough at times. However, trigonometry and trigonometry formulas, if understood properly, are very interesting concepts. Important applications like measurement of the altitude of Mount Everest, measurement of the height of various buildings, etc have been facilitated with the help of trigonometry only. In this article, we will go through the concepts of trigonometry and trigonometry formulas. We will also see how this mathematical branch developed during the course of human history.

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