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June 30, 202239 Insightful Publications

If you love gazing at the stars from your balconies and have wondered how far the stars are from you, the answer to this question lies in Trigonometry. Trigonometry is the branch of Mathematics that explains the relationship between the sides and angles of the triangle. Initially, it was restricted to right angles only, but the concepts of Trigonometry were later expanded to include other types of triangles. In this article, you will learn what Trigonometry is, some interesting stories about its origin, and how to master it.

What better way to start the introduction to Trigonometry other than getting to know the origin of the What better way to start the introduction to Trigonometry than getting to know the origin of the word itself? The word ‘Trigonometry’ is derived from three different Greek words: ‘ tri’, ‘three’, ‘gon’, ‘angle’, and ‘metr’, which means ‘to measure’. Together these words mean ‘measurement of three angles of a triangle.

It is believed that the origin of Trigonometry was the civilisations of ancient Egypt, Indus valley, and Mesopotamia, approximately 4000 years ago. It is worth noting here that the Babylonians used 60 as the base for their numerical system, and this was the common practice used even for the calculation of sides and angles of the triangle.

Hipparchus was a Greek astronomer and a mathematician who made profound contributions to both fields. He is known as the ‘founder of trigonometry’ as he was the first to compile a trigonometric table for solving the sides and angles of triangles. This story dates back to 150 B.C.E.

Many great Indian mathematicians like **Bhaskara**, **Aryabhata**, **Brahmagupta**, and **Srinivasa Ramanujam** have made profound contributions to the world of Mathematics. They are recognised and remembered even today for their path-breaking discoveries, such as the concept of Infinity, elliptic functions, and the discovery of ‘*zero*‘.

Coming to Trigonometry, it is worth remembering the accomplishments of Aryabhata, who gave to the world the tables of sines and cosines. Another great mathematician Brahmagupta is known for his numerous contributions, including how to calculate the area of a triangle, sin function, and also the formula for cyclic quadrilaterals. His work on cyclic quadrilaterals was greatly appreciated by other mathematicians of his period and formed the basis for other discoveries to be made later.

As mentioned at the beginning, Trigonometry deals with the relationship between a triangle’s sides and angles. Trigonometric functions, therefore, are the functions that denote this relationship. There are six trigonometric functions – **Sine, Cosine, Tangent, Secant, Cosecant and Cotangent.**

Trigonometric functions are the earliest forms of mathematical tables. In schools, you are taught how to use trigonometry tables and look for the correct answer using corresponding rows and columns. It is even possible to look for fetching the in-between values to not compromise on the accuracy of the results.

However, for someone learning about the Trigonometric functions, you can use the mnemonic **SOH-CAH-TOA **for easy reference. The mnemonic is based on the different sides of the triangle, namely Opposite, Adjacent, and Hypotenuse, all concerning the right angle of the triangle.

**S**ine =** O**pposite + **H**ypotenuse

**C**osine =** A**djacent + **H**ypotenuse**T**angent = **O**pposite + **A**djacent

A few other mnemonics are also available. However, this is the most commonly used.

The list of applications of Trigonometry and Trigonometric function is endless. One can find its applications in astronomy, construction, Physics, Engineering (specifically, Aeronautical Engineering), and the creation of video games.

You’ll be surprised to learn that criminal case investigators use Trigonometry concepts for analysing the crime scene. Therefore, you can see that Trigonometric functions have a significant role in catching the culprits.

Calculating the path taken by a vehicle in case of an accident to the angle at which the gun was shot or how an object might have fallen from a height, trigonometric functions can help criminologists solve challenging cases.

Another important use of Trigonometry that you can think of, especially as students who use maps in schools to look up various places, is how a map is constructed based on the location and orientation of different geographical locations concerning one another.

Some students find Trigonometry very interesting and easy, whereas it may appear tough for others. As an important branch of Mathematics carrying high weightage in the Class 10 board exam, it is important to have an in-depth understanding of trigonometric functions and solve problems of different types to master the subject.

Here are four tips that will help you master trigonometric functions in your exam.

- Understand the concepts behind trigonometric functions – As you might have already understood by now, trigonometric functions are like the building blocks for understanding everything else about Trigonometry. Another interesting fact to note here is that these functions are interrelated. Once you crack the relationship between them, everything from there becomes easy.
- Know the real-life applications of Trigonometry – Any concept becomes interesting and easy if you learn about its applications, especially in our daily lives. This way, you’ll be able to relate to and remember the topics easily. For example, if you have seen how a sine wave is represented on a graph sheet, you will remember that the movement of a spring bouncing back and forth can be compared to how trigonometric functions are represented on a graph.
- Learn and revise often – If you still have trouble understanding Trigonometry, do not be discouraged. Some concepts require a second and the third reading for proper understanding, and the same is the case with trigonometry for most students. Make notes while studying and keep them handy for future reference, practice as many questions as possible and keep learning the formulas regularly.
- Focus on formulas and derivation methods – It is almost impossible to remember every Trigonometrical formula; frankly, there is no need to do that. This is because the formulas can be derived from one another. You cannot go wrong if you know a few basic formulas and understand how the other one is connected to this.

**We hope that this article on trigonometry was of immense help. For more such interesting articles on Trigonometry and Trigonometric functions, follow Embibe.**