# INTRODUCTION TO TRIGONOMETRY

#### Trigonometry Meaning • Trigonometric Ratios • Trigonometric Identities

“TRIG” COURSE – PART-1

INTRODUCING TRIGONOMETRY: Students after starting to listen the word ” Trigonometry ” from class 9. Moreover, our basic Trigonometry courses starts from Class 10. Some students feels that trigonometry is one of the tough chapter from Mathematics, on the other hand, for some students, it is the easiest chapter ever. But, the actual thing is that really it’s one of the most interesting and the easiest chapter, if you clear all the concepts, finally, you can obviously feels it easier. After all, here we try our best to deliver all the clear concepts, specially, What is meant by trigonometry and what is the meaning of Trigonometry in simplest format of text.

Firstly, Trigonometry starts from Class 10, but it never ends. There is a big chain. There is a big importance of it. Without trigonometrical concepts, you can never start a higher classes in any numerical contents. When you are going to study Algebra, Co-ordinate geometry, spaces, complex number, derivatives, limit, integration – you must need full concepts of it. You can’t imagine these contents without it. Hereby, from this single post, we are starting our new course “Trig” with VIDEO TUTORIALS.

Course : “Trig”  Part – 1

## WHAT IS TRIGONOMETRY?

Firstly, after listening the word TRIGONOMETRY, the first line, that often comes in our mind  is that WHAT WHAT IS TRIGONOMETRY? or WHAT IS MEANT BY TRIGONOMETRY? Well, here we are giving the meaning of Trigonometry is simplest words-

 Trigonometry is one of the major content of Mathematics, where we discuss about the ratios of any two sides of a right angular triangle, with respect to any one of the angle, except the right angle.

 Trigonometry Comes From Greek Words “trigon” and “mitron” and it means “measuring the sides of a triangle” . Moreover, “Tri” means Three, “gono” means Sides and “metry” means Measurements. So. Somple meaning is “Measurements Of Three Sides Of A Triangle”

This is the Meaning of Trigonometry is simple words. Remember, this is just a content of Maths, a major part of Mathematics, where we will discuss about the ratios of any two sides of a right angular triangle.

### What is trigonometry in hindi :

त्रिकोणमिति गणित की प्रमुख सामग्री में से एक है, जहाँ हम समकोण त्रिभुज के किसी भी दो पक्षों के अनुपात के बारे में चर्चा करते हैं, समकोण के अलावा किसी भी एक कोण के संबंध में।

त्रिकोणमिति ग्रीक शब्द “ट्रिगॉन” और “मिट्रॉन” से आती है और इसका अर्थ है “त्रिकोण के पक्षों को मापना”। इसके अलावा, “त्रि” का अर्थ है तीन, “गोंओ” का अर्थ है साइड्स और “मेट्री” का अर्थ है माप। इसलिए। सोम्पल का अर्थ है “त्रिभुज के तीन पक्षों की माप”

## WHAT IS TRIGONOMETRIC RATIOS?

We often listening about TRIGONOMETRIC RATIOS . Actually what are these? Nice! These are nothing but only the ratios, that we have just studied in the Meaning Of Trigonometry.

That means, the ratios of any two sides of a right angular triangle with respect to any one of the angle other than the 90° angle, are the Trigonometric Ratios. For any two given sides, we can get 2 ratios. For example – For Base & Perpendicular, we can get two ratios: “Base isto Perpendicular” and “Perpendicular isto base”.

Thus, there are three sides in a triangle, that’s why we can get Six Trigonometric Ratios . Our Mathematician Named these Trigonometric Ratios as – Sine, Cosine, Tangent, CoTangent, Secant and Cosecant. Usually, we express them in short forms as – Sin, Cos, Tan, Cot, Sec and Cosec respectively. We will discuss about these Six Trigonometric Ratios briefly in bellow section.

### Trigonometric Ratios in hindi

90 ° कोण के अलावा किसी भी एक कोण के संबंध में एक समकोण त्रिभुज के किसी भी दो पक्षों के अनुपात, त्रिकोणमितीय अनुपात हैं। किसी भी दो पक्षों के लिए, हम 2 अनुपात प्राप्त कर सकते हैं। उदाहरण के लिए – आधार और लम्बवत् के लिए, हम दो अनुपात प्राप्त कर सकते हैं: “Base isto Perpendicular” और “Perpendicular isto base“। इस प्रकार, त्रिभुज में तीन भुजाएँ होती हैं, इसीलिए हम छह त्रिकोणमितीय अनुपात प्राप्त कर सकते हैं। हमारे गणितज्ञ ने इन त्रिकोणमितीय अनुपातों को नाम दिया है – Sine, Cosine, Tangent, CoTangent, Secant and Cosecant। आमतौर पर, हम उन्हें छोटे रूपों में व्यक्त करते हैं – Sin, Cos, Tan, Cot, Sec और cosec । हम इन छह त्रिकोणमितीय अनुपातों के बारे में संक्षिप्त रूप से चर्चा करेंगे।

## What is the Use of Trigonometry?

Secondly, the next question that appears in our mind after knowing the Meaning of Trigonometry – why is Trigonometry important? What is the use of Trigonometry? What are the benefits of studying Trigonometry? Well, the answer is in bellow portion.

We can determine some distances, without actual measurements, using Trigonometric identities. For Example, if we know the shadow length of a tree or a tower and the inclination angle made by the sunlight, which can be determined using other practical method easily. Then we can find the height of the tree or the tower very very easily using Trigonometric identities, which was firstly impossible or difficult to find. Moreover, It is often use to find Refractive index too. Thus, The role of Trigonometry in our daily life is too much important.

## Six Trigonometric Ratios :

We have just studied that the Six Trigonometric ratios are Sine, Cosine, Tangent, CoTangent, Secant and Cosecant. In short, they are – Sin, Cos, Tan, Cot, Sec and cosec. Bellow is the First most important table to be discussed if you want to clear all the concepts of Trigonometry. Where we have listed the ratios with their respective sides. Before that, Lets recognise the hypotenuse, Base and Perpendicular of a right angular triangle now.

 The trigonometric ratio “Tangent” comes from Latin word “Tangere” which means “to touch” . Moreover, Each of these six trigonometric ratios have a complementary function, flagged by the prefix “co-“, that comes from a “Latin word Prefix” which means “jointly” or “together”. Thats why, we also have the alt Trigonometric Ratios cosine, cosecant and cotangent

We assume a triangle ABC bellow with angle B = 90°. We will find the ratios w.r.t. angle “A”. • Hypotenuse (H) : The side, Directly opposite to 90°, is the hypotenuse. AC is the hypotenuse in ∆ABC.
• Base (B) : The side, that connects the given angle, (w.r.t. which we will find the ratio) and the 90° angle, is the base. AB is the base in ∆ABC.
• Perpendicular (P) : The rest third side is the Perpendicular. BC is the Perpendicular in ∆ABC. Then, Remember the bellow table:

## TRIGONOMETRIC INDENTITIES TABLE – 1

 Sin Perpendicular / hypotenuse P / H Cosec hypotenuse / Perpendicular H / P Tan Perpendicular / Base P / B Cot Base / Perpendicular B / P Cos Base / hypotenuse B / H Sec hypotenuse / Base H / B 