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What is Trigonometry?


Trigonometry is a separate branch of mathematics, which deals with triangles. It also studies the relationship between their sides and angles, by defining the separate trigonometric functions. The trigonometric functions are universally adopted in the part of pure mathematics and applied mathematics. The introduction to trigonometry is quite simpler. The basis of its function depends upon right angled triangle. Hence, to make a complete angle, two acute angles are added to the 900. These are known as complementary angles. If the length of the one side is given, then we can easily determine the other two sides of the triangle. Now, we will see what is trigonometry.

The ratios of trigonometry are given with the help of the following trigonometric functions. If any one angle is known, suppose angle ‘C’, then we can find the sides of the triangle, where x, y, z are considered as the sides of the triangle.

There are six trigonometric functions: sine, cosine, tangent, secant, cosecant, cotangent.

  • Sine function (sin) can be defined as the ratio of altitude (opposite side to the angle) to the hypotenuse (the longest side). Sin C = $\frac{\text{Altitude}}{\text{Hypotenuse}}$.
  • Cosine function (cos) is defined as the ratio of the base to the hypotenuse. Cos C = $\frac{\text{Base}}{\text{Hypotenuse}}$.
  • Tangent function (tan) can be defined as the ratio of altitude to the base. Tan C = $\frac{\text{Altitude}}{\text{Base}}$.
Functions such as cosecant (cosec), secant (sec), cotangent (cot) are reciprocal of the above mentioned functions respectively.
  • Cosec C = $\frac{1}{\text{sin C}}$
  • Sec C = $\frac{1}{\text{cos C}}$
  • Cot C = $\frac{1}{\text{tan C}}$ = $\frac{\text{cos C}}{\text{sin C}}$
Above trigonometry definition is applied to the angles between 00- 900. There are many fields in which these trigonometric functions are useful such as, in the field of astronomy, navigation, seismology, medical imaging(ultrasound) and many more.

History of Trigonometry

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We all study trigonometry in math and also know about the different functions of the trigonometry and we all generally know about the applications of these functions. But, most of us are generally not familiar with the history of trigonometry which is many years old. Let us recall the history of trigonometry and discuss about how the trigonometry was introduced and also about the various developments which took place in the history of trigonometry with the time.

The history of trigonometry starts from a very earlier period of the second century of BCE during which the topic of the trigonometry was first introduced by the great mathematician of Greece whose name was Hipparchus. The history of trigonometry and the history of the trigonometric functions have followed the common lines of the history of the math.

Now, let us start with triangles. The first discussion about triangles in the history of trigonometry was held in the math of the Egypt during the period of the second millennium of BC and was also found in the math of the Babylon. However, the discovery of the trigonometric functions and their proper study was started from the Hellenistic math which was introduced in India as a section of the astronomy. The development of the history of trigonometry in India with the help of introduction and the proper study of the trigonometric functions was done in the period of the Guptas and was mostly credited to the great Indian mathematician Aryabhata, who developed the math in India to a great level in the sixth century and in the history of trigonometry. During the period of the middle ages, the development of the trigonometry was further carried by the math of the Islam.