# NCERT Solutions for Class 10 Maths Chapter 8 Introduction to Trigonometry

## NCERT Solutions for Class 10 Maths Chapter 8 Introduction to Trigonometry - Free PDF

NCERT Solutions Class 10 Maths Chapter 8 Trigonometry is one of the important lessons for your board exams and our faculties have put in a lot of effort to provide you with revised solutions and important facts related to the Chapter 8 Maths Class 10. All the important formulas and problems have been laid out in a sequential manner, thus ensuring a thorough review of all the important topics in the ch 8 Maths Class 10 Trigonometry. The solutions provided by our faculties would help you to help you score high marks in exams. The solved answers to Chapter 8 Exercises will help you immensely for as long as you study Maths. Use Vedantu’s NCERT Book solutions for CBSE Class 10 Maths Chapter 8 Exercises and score big in your Maths test. Download the Free PDF on Class 10 mathematics Chapter 8 Exercises as per your requirement. Students can also find Class 10 Science Solutions on Vedantu.

## NCERT Solutions for Class 10 Maths Chapter 8 Introduction to Trigonometry - PDF Download

You can opt for Chapter 8 - Introduction to Trigonometry NCERT Solutions for Class 10 Maths PDF for Upcoming Exams and also You can Find the Solutions of All the Maths Chapters below.

NCERT Solutions for Class 10 Maths

About the Chapter - Introduction to Trigonometry

As the name suggests, trigonometry is all about triangles. To be more specific, it is more about right- angled triangles, the triangles with one angle equal to 90 degrees. It is a system that helps us to find missing angles and missing sides of a triangle. The word trigono means triangle and the word metry means measure.

The Chapter 8 Introduction to Trigonometry of Class 10 NCERT Syllabus is divided into five sections and four exercises where the last exercise section consists of problems with hints. The first section is the basic introduction to trigonometry Class 10 having examples from the surrounding where the right angle triangle can be imagined.

The second section consists of an introduction to trigonometric ratios along with the derivation of sine, cosine and other trigonometric functions with examples and followed by an exercise at the end of the section.

The third section consists of Trigonometric ratios with respect to different measures of angles. The fourth section in Chapter 8 Class 10 Maths consists of criteria for trigonometric ratios for complementary angles with a few solved examples, and it ends with an exercise.

The fifth section consists of the topic related to the trigonometric identities in introduction to trigonometry class 10, with a few examples and ends with an exercise.

After this section comes the exercise section in chapter 8 Maths Class 10 trigonometry where extra sums are provided for you to solve and be thorough with the concepts. The topic ends with a summary which covers up all the important points.

Introduction to Trigonometry

List of exercise and topics covers in this chapter class 10 trigonometry:

Section 8.1: Introduction to trigonometry class 10.

Section 8.2 : Trigonometric Ratios

Exercise 8.1: Questions related to Trigonometric Ratios. The exercise consists of 11 sums.

Section 8.3: Trigonometric Ratios for some specific angles.

Exercise 8.2: Questions related to the Trigonometric Ratios for some specific angles. This exercise has 4 sums.

Section 8.4 : Trigonometric Ratios of Complementary angles

Exercise 8.3: Questions related to the Trigonometric Ratios of Complementary angles. The exercise consists of 7 sums.

Section 8.5 : Trigonometric Identities

Exercise 8.4: Questions related to Trigonometric Identities. The exercise consists of 5 sums.

In this ch 8 Maths class 10, we will be learning about trigonometry, its ratios and identities and at the end, we have given the summary of the entire chapter.

What Is A Right-angled Triangle In Ch 8 Maths Class 10

The little box in the corner of the triangle denotes the right angle which is equal to 90°.

The side opposite to the right angle is the longest side of the triangle which is known as the hypotenuse (H).

The side that is opposite to the angle θ is known as the opposite (O).

And the side which lies next to the angle is known as the Adjacent(A).

According to Pythagoras theorem, we know that,

In a right-angle triangle, (\[Opposite^{2}\]) +(\[Adjacent^{2}\])= (\[Hypotenuse^{2}\])

Historical Facts – Let’s Turn the Pages of History!

The Babylonians could measure angles, and are believed to have invented the division of the circle into 360º.However, it had been the Greeks who are seen because the original pioneers of trigonometry.

A Greek mathematician, Euclid, who lived around 300 BC (Before Christ), was a crucial figure in geometry and trigonometry. He's most famous for Euclid's Elements, a really careful study in proving more complex geometric properties from simpler principles. Although there's some doubt about the originality of the concepts contained within Elements, they're influential in how we expect about proofs and geometry today; indeed, it's been said that the elements have “influence upon the human mind greater than that of the other work present except the Bible.

The first trigonometric table was compiled by Hipparchus in the early ages (180-125 BCE), who is now known as "the father of trigonometry”. He was the first man to tabulate the corresponding values of arc and chord for a series of angles.

Trigonometric Functions in Chapter 8 Maths class 10- Basically, there are six functions that are the core of trigonometry chapter 8 Maths class 10. There are three primary ones also known as the basic ones in ch 8 Maths class 10 which are important to understand completely:

Sine (sin)

Cosine (cos)

Tangent (tan)

The other three trigonometric functions are not used as often and these three functions can be derived from the three primary functions (sin, cos, tan). Because these can easily be derived, calculators and spreadsheets do not usually have them.

Cosecant (cosec)

Secant (sec)

Cotangent (cot)

All six functions in ch 8 Maths class 10 have a three-letter abbreviation which is written just next to them within the parenthesis.

## The Six Functions of Trigonometry in Ch 8 Maths Class 10:

NAME | ABBREVIATION | FORMULA |

Sine | Sin | Sin (θ)= Opposite/Hypotenuse |

Cosine | Cos | Cos (θ)= Adjacent/Hypotenuse |

Tangent | Tan | Tan (θ)= Opposite/Adjacent |

Cosecant | Cosec | Cosec ( θ)= Hypotenuse/Opposite |

Secant | Sec | Sec ( θ) = Hypotenuse /Adjacent |

Cotangent | Cot | Cot ( θ) = Adjacent / Opposite |

What are the three functions Sine, Cosine, Tangent in ch 8 Maths class 10?

Sine: Sine of an angle can be defined as the ratio of the side opposite to the angle (θ) to the hypotenuse (longest side) in the triangle.

Cosine: Cosine of an angle can be defined as the ratio of the side which is adjacent to the angle (θ) to the hypotenuse (longest side) in the triangle.

Tangent: Tangent of an angle can be defined as the ratio of the side which is opposite to the angle (θ) to the adjacent in the triangle.

Tricks to Remember the Formulas

SOH, COH and TOA is a mnemonic way or trick to remember the three basic trigonometric ratios defined by the trigonometric ratio definition.

SOH stands for Sine equals Opposite over Hypotenuse. (Sin (θ)= Opposite/Hypotenuse) |

CAH stands for Cosine equals Adjacent over Hypotenuse. (Cos (θ)= Adjacent/Hypotenuse |

TOA stands for Tangent equals Opposite over Adjacent. (Tan (θ)= Opposite/Adjacent) |

These nine letters are a memory aid and would help you to remember the ratios for the three basic functions Sine, Cosine and Tangent. Well, we can pronounce it as “sohcahtoa”.

Now that you have understood the important points in the chapter, you should also know that there is a pattern in the examination to test the knowledge of the students and to check their capabilities to perform better in future. When you understand the NCERT Class 10 Introduction to Trigonometry chapter 8, it helps you understand the points you need to focus on - like the weightage of the chapter, the number of questions appearing in the exam - and helps you [prepare better for your exam. Practicing these NCERT solutions helps you speed up solving the problems and helps you keep up with time and ensure you finish your entire paper within the given duration.

As they say, practice makes you perfect, NCERT ensures that you achieve perfection to complete your papers and increase the speed in solving your problems. You will know what kind of problems might come to your exam and the number of questions from this particular question. This will help you strategize better to score better marks and gauge the frequency of the questions. Most of the time, the questions are usually repeated and solving the previous question papers will help you solve these questions faster. Most of the time, only the numbers are changed and the questions are a little bit twisted. By using the aforementioned points, you will be able to score at least 90% in your exams.

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Vedantu is an ardent believer of smart work and harbour experienced teaching professionals who are adept at learning .The professionals at Vedantu possess a greater passion for imparting the same. Vedantu aims at making the learning experience fun by offering solutions in a step by step explanation of numerical problems which will make it easier for you to understand the topic and grasp the concept. The step by step solution makes it easy for the students to solve difficult problems. This solution presented is engineered by the experts of Vedantu to serve it as an excellent material for practice and it helps to make the learning process more convenient.

The main strength of the Vedantu’s NCERT Solutions for Class 10 Maths Introduction to Trigonometry lies in the following points:

Solutions are written keeping in mind the age group of the students so that it would be easy for them to understand.

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It gives a gist of the entire chapter and concept in the form of solutions. This would help you to revise the topic in an efficient manner.

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Topics and answers are incorporated with necessary images to facilitate the understanding of the concept.

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Vedantu tries its best to render you real help by providing the NCERT Solutions for Class 10th Maths Chapter 8 Introduction to Trigonometry. It aims to deliver sufficient problems and solutions to practice and build a strong foundation on the chapter.

Why do we need Trigonometry?

This is an inexpensive question, and therefore the answer is because those that decide the mathematics curriculum in many countries think that you simply should know about it.

However, it does even have a couple of real-life functions, perhaps the foremost obvious of which is navigation, especially for boats.

1) Trigonometry and Navigation

When you are sailing or cruising stumped, where you finish up is affected by:

1)The direction during which you steer.

2) The speed at which you travel therein direction (i.e. the motor or wind speed)

3) The direction and speed of the tide. You can be motoring in one direction, but the tide might be coming from one side, and push you to the opposite. You'll need trigonometry to figure out how far you'll travel and in what precise direction.

Note: It should be noted that Sec (θ) does not refer to the product of Sec and θ. Sec ( θ) is correctly read as secant of angle ( θ).

2. Trigonometry and Geometry

Trigonometry has its application in geometry too; it is mainly used to solve triangles, usually right-angled triangles. That is, given some angles and side lengths, we can find some sides or all the missing ones.

For example, see the figure given below, if we know the height of the tree and the angle made when we look up at its top, we can easily calculate how far away it is (Using our full toolbox, we can actually calculate all three sides and all the three angles of the right triangle named ABC).

3. Advanced Use of Trigonometry

In a more advanced use, the trigonometric ratios such as Sine and Tangent, can be used as functions in equations and are easily manipulated using algebra. In this way, trigonometry has many engineering applications such as electronic circuits and mechanical engineering. In this analytical application, trigonometry basically deals with angles drawn on a coordinate plane, and it can also be used to analyze things like motion and waves.

For example, we can describe a radio or sound wave can by an equation such as:

y=sin (ax+b) and when we graph the equation it might look something like the wave given below. The value a determines the wave's amplitude, b determines the frequency and c determines the phase shift.

4. Trigonometry is used in cartography which is the creation of maps.

5. It has its applications in satellite systems.

6. It is used in aviation industries.

The following relations are obvious from the definition of trigonometric ratios and are important for 10th Maths trigonometry:

## Trigonometric Relations:

Tan (θ)= | \[\frac{Sin(\theta)}{Cos(\theta)}\] |

Sec (θ)= | \[\frac{1}{Cos(\theta)}\] |

Cot ( θ)= | \[\frac{Cos(\theta)}{Sin(\theta)}\] |

Cosec ( θ)= | \[\frac{1}{Sin(\theta)}\] |

What are Trigonometric Ratios?

Trigonometry identities are the trigonometry equation that comprises the trigonometry ratios of all the angles.

They can be formulated through a right angle triangle.

We can express each trigonometric ratio in the terms of another trigonometric ratio.

If one of the values of trigonometry ratio is known we can find out the other value of the trigonometry ratio easily.

They can also be used to acquire the various trigonometry formulas.

Here’s a table showing the value of each ratio with respect to different angles. These ratios are used in different calculations and are important for solving various problems.

The table given below shows the value of each ratio with respect to different angles.

Angle | 0 ° | 30 ° | 45 ° | 60 ° | 90 ° | 180 ° | 270 ° | 360 ° |

Sin | 0 | 1/2 | 1/√2 | √3/2 | 1 | 0 | -1 | 0 |

Cos | 1 | √3/2 | 1/√2 | ½ | 0 | -1 | 0 | 1 |

Tan | 0 | 1/√3 | 1 | √3 | ∞ | 0 | ∞ | 0 |

Cot | ∞ | √3 | 1 | 1/√3 | 0 | ∞ | 0 | ∞ |

Cosec | ∞ |
2 | √2 | 2/√3 | 1 | ∞ | -1 | ∞ |

Sec | 1 | 2/√3 | √2 | 2 | ∞ | -1 | ∞ | 1 |

Here are the tricks to remember the above values:

Step 1: Divide the numbers 0, 1, 2, 3 and 4 by 4,

Step 2: Take the positive square roots of each of them.

Step 3: These numbers will give the values of sin 0°, sin 30°, sin 45°, sin 60° and sin 90° respectively.

Step 4: Write down the values of sin 0°, sin 30°, sin 45°, sin 60° and sin 90° in reverse order and now you will get the values of cos , tan , cosec , sec and cot ratios respectively.

Here’s a little description about how we got the values. Let's take an acute angle θ, we know that the values of sin θ and cos θ lies between 0 and 1.

The sin of the standard angles 0°, 30°, 45°, 60° and 90° are the positive square roots of 0/4,1/4, 2/4,3/4 and 4/4 respectively.

Radians vs Degree in Trigonometry Class 10:

In geometric applications, the argument of a trigonometric function can be generally defined as the measure of any angle. For this purpose, we can use any angular unit which is convenient, and we basically measure the angles in degrees.

In Calculus whenever we use any trigonometric function, their argument is generally not an angle, but rather the argument is a real number. In such cases, it is better if we express the argument of the trigonometric as the length of the arc of the unit circle as we have discussed above, delimited by an angle considering the vertex as the center of the circle. Therefore, radian can be used as an angular unit: a radian can be defined as an angle that delimits an arc of length one on the unit circle. A complete turn is thus equal to an angle of 2π radians.

A great advantage of radians is that it makes the application of formula easier, typically all formulas which are relative to derivative and integrals.

Thus, we can say that using radian as the unit makes everything simpler.

## The Different Values of sin, cos, and tan with Respect to Radians have been Listed Down in the Table Given Below-

Angle | 0° | 30° | 45° | 60° | 90° | 180° | 270° | 360° |

Radian | 0 | π/6 | π/4 | π/3 | π/2 | π | 3π/2 | 2π |

## Reciprocal Relations between the Trigonometric Functions-

sin (x) can be written as 1 / Cosec(x) | cosec (x) can be written as 1 / Sin(x) |

Cos (x) can be written as 1 / sec(x) | sec(x) can be written as 1 /Cos(x) |

tan (x) can be written as 1 /cot(x) | cot (x) can be written as 1 /tan(x) |

From these results, it follows that,

1. | Sin x• cosec x =1 |

2. | cos x• sec x =1 |

3. | tan x• cot x =1 |

## Basic Trigonometric Identities-

Sin 2(θ)+cos 2(θ)= | 1 |

Tan2(θ)+1= | Sec2(θ) |

Cot 2(θ)+1= | Cosec2(θ) |

## Here are the Opposite Real Number Identities for Trigonometry Class 10 -

1. | Sin(-x) = - sin x |

2. | Cos(-x) = cos x |

3. | Tan(-x) = -tan x |

4. | Cot(-x) = -cot x |

5. | Sec(x) = sec x |

6. | Cosec(-x) = -cosec x |

VARIATIONS IN VALUES OF TRIGONOMETRIC FUNCTIONS IN DIFFERENT QUADRANTS:

There are four quadrants in Mathematics. The coordinate axes basically divide the plane into four quadrants, which are labeled first, second, third and fourth as shown. Angles in the first quadrant lie between 0 degrees and 90 degrees, second quadrant lies between 90 and 180 degrees, third quadrant lies between 180 degrees and 270 degrees and the fourth quadrant lies between 270 and 360 degrees.

What is an Angle in a Quadrant in Trigonometry Class 10?

An angle in a quadrant is known to be in a particular quadrant, if the terminal side of a given angle in standard position lies in that quadrant.

## The Range of the Different Functions in each of the Quadrants:

I QUADRANT | II QUADRANT |

Sin increases from 0 to 1 Cos decreases from 1 to 0 Tan increases from 0 to Cot decreases from to 0 Sec increases from 1 to Cosec decreases from to 1 | Sin decreases from 1 to 0 Cos decreases from 0 to -1 Tan increases from - to 0 Cot decreases from 0 to -∞ Sec increases from - to -1 Cosec θ decreases from 1 to |

III QUADRANT | IV QUADRANT |

Sin increases from 0 to -1 Cos decreases from -1 to 0 Tan increases from 0 to Cot decreases from to 0 Sec decreases from -1 to - Cosec θ decreases from - to -1 | Sin increases from -1 to 0 Cos increases from 0 to 1 Tan increases from -∞ to 0 Cot decreases from 0 to -∞ Sec decreases from ∞ to 1 Cosec θ decreases from -1 to |

Important Trigonometry Formulae in trigonometry Class 10:

The Trigonometric formulas or Identities are the equations which are true only in the case of Right-Angled Triangles.

Some of the important trigonometric identities are as given below –

## Pythagorean Identities:

sin² θ + cos² θ = | 1 |

tan2 θ + 1 = | sec2 θ |

cot2 θ + 1 = | cosec2 θ |

sin 2θ = | 2 sin θ cos θ |

cos 2θ = | cos² θ – sin² θ |

tan 2θ = | 2 tan θ / (1 – tan² θ) |

cot 2θ = | (cot² θ – 1) / 2 cot θ |

Sum and Difference identities-

## For Angles m and n, we have the Following Relationships:

Sin (m+ n) = | sin(m)cos(n) + cos(m)sin(n) |

Cos (m +n) = | cos(m)cos(n) – sin(m)sin(n) |

Tan (m +n) = | tan(m) + tan(n)/1−tan(m) tan(n) |

Sin (m – n) = | sin(m)cos(n) – cos(m)sin(n) |

Cos(m – n) = | cos(m)cos(n) + sin(m)sin(n) |

Tan (m-n) = | tan(m) − tan(n)1+tan(m) tan(n) |

Trigonometry in a Circle

The Cartesian Coordinates of a circle. Let us consider a circle, divided into four quadrants.

Conventionally, the centre of the circle is taken into account has a coordinate of (0, 0). That is, the x value is 0 and therefore the y value is 0 at the centre of the circle.

Anything to the left of the centre has the x value less than 0, or is negative, while anything to the right has a positive value of x.

Similarly anything below the centre point has a y value of less than 0, or is negative and any point in the top of the circle has a positive value of y.

Rotate the radius to make the Sin, cos and Hypotenuse. Now consider what happens if we draw a radius from the centre of the circle, east if the circle were a compass. It is marked as 1 within the diagram.

If we then rotate the radius around the circle in an anticlockwise direction, it'll create a series of triangles:

At point 2, we can see a right-angled triangle. θ is around 60°.

Sin θ is the opposite (denoted by the red line in the above figure) / the hypotenuse (denoted by the blue). Cos θ is the adjacent (denoted by the green line) over the hypotenuse (denoted by the blue).

At point 3, θ is an obtuse angle, which lies between 90° and 180°. Sin θ is the red line over the hypotenuse, and therefore the value of sin will be positive. Cos θ being the green line over the hypotenuse, will be negative as we know that the green line is negative to the left of 0.

As we rotate the radius around the circle, the other two internal angles and the length of the other two sides vary and therefore affect the value of the sin and cos.

## The Table Below Shows the Three Basic Trigonometric Functions

NAME | ABBREVIATION | RELATIONSHIP |

Sine | Sin | Sin (θ)= Opposite/Hypotenuse |

Cosine | Cos | Cos (θ)= Adjacent/Hypotenuse |

Tangent | Tan | Tan (θ)= Opposite/Adjacent |

What is a Unit Circle?

A unit circle can be defined as a circle with radius equal to 1.

While working with a unit circle we can easily find out the measures of Sine, Cosine and Tangent.

Graphs of Sine, Cosine, Tangent, Secant, Cotangent, Cosecant:

Graph for sin (θ)

Graph for Cos (θ)

Graph for Tan (θ)

The Graph of Sin and Cos:

The relationship between the angle of sin or cos can be drawn as a graph:

y = sin(x)

y = cos(x)

Fun Facts About Trigonometry:

1. Trigonometry is used by engineers to figure out the angles of the sound waves and how to design rooms.

2. A Mathematician named Hipparchus produced the first known table of chords in the 140 BC

3. The most ancient device found in all early civilizations in a 'Shadow Stick', generally casted shadows which was used to observe the motion of the Sun, thus telling the time.

4. Babylonians, the Egyptians, based Trigonometry on their base 60 numeral system in the early age.

5. The word "Trigonometry" comes from the word "Triangle Measure” and is related to the measurement of sides and angles of a triangle.

Understanding the Exercises and Sections

Every topic is followed by an exercise which consists of topics that are related to the information given in that section. The reason why there are exercises after every topic is to ensure that you grasp the concept that is being taught in the sections. Most of the problems in this chapter are based on formulas that are explained in every section of the topic.

To help you further in understanding these topics and the concepts related to this topic better, a good number of solved examples are explained after every section. In addition to that, step by step explanation of these problems is also shown for every example. This helps in choosing the best approach to solve different types of problems.

Section 8.1

This section gives an introduction to trigonometry. It reminds you of what has been taught to you in your previous grades and also explains the prerequisites for this chapter. Some basic definitions, properties and examples are given in this section. Besides that, you will understand how to calculate the measures of sides.

Section 8.2 - Exercise 8.1

In this section, you learn mostly about trigonometric ratios. The way how we get the formulas of trigonometric functions has been explained. The key point explained in this section is how we derive the values of sine, cosine and tangent from a right-angled triangle .The section tells us that sine of an angle can be defined as the ratio of the side opposite to the angle (θ) to the hypotenuse (longest side) in the triangle whereas cosine of an angle can be defined as the ratio of the side which is adjacent to the angle (θ) to the hypotenuse (longest side) in the triangle and tangent of an angle can be defined as the ratio of the side which is opposite to the angle (θ) to the adjacent in the triangle.

In the exercise 8.1, you have eleven problems. The questions are generally based on the formulas of Pythagoras Theorem and the values of different sides.

Section 8.3 - Exercise 8.2

Here, you will be learning only about the trigonometric ratios of different angles. The common angles are 0, 30, 45, 60 and 90 degrees. The exercise consists of four problems which are further divided into various sub problems.

In Exercise 8.2, the questions are mostly based on finding the ratios of angles of a triangle. Some questions have the measurements of the sides of the triangle. The last questions is a true or false objective type question to test your understanding. To conclude, there are total four questions in this exercise.

Section 8.4-Exercise 8.3

This section consists of trigonometric Ratios of Complementary angles. It has how we can derive the different values of sine, Cosine and Tangent of complementary angles (90-A). The section consists of various examples. The exercise consists of 5 sums which revolve around finding the trigonometric ratios of angles less than 90 degrees.

Section 8.5 Exercise 8.4

This section consists of trigonometric identities which can be defined as an equation when it is true for all values of the variables involved. Similarly, an equation involving trigonometric ratios of an angle is known as Trigonometric identities. Again, in this section, there are around five questions which asked you to justify the correct answer. Or in other words, the first question is to express the trigonometric ratios for various trigonometric ratios, proving the different trigonometric identities. Question number four is a MCQ question where you need to choose the correct option.

Summary

In this chapter, here are the points you need to keep in mind :

1) Suppose we have a right triangle MNP, right-angled at N ,

sin M =side opposite to angle M /hypotenuse,

cos M = side adjacent to angle M /hypotenuse

tan M = side opposite to angle M/ side adjacent to angle M

2) cosec M = 1/sin M , sec M = 1/cos M , cot M = 1/tan M

3) If any one of the trigonometric ratios of an acute angle is known in a triangle, then the remaining trigonometric ratios of the angle can be easily determined by using all the concepts you have gone through.

4)The values of trigonometric ratios for angles 0°, 30°, 45°, 60° and 90° are very important and can be used in various problems.

5) The value of sin M or cos M never exceeds 1, whereas the value of sec M or cosec M is always greater than or equal to 1.

6) sin (90° – M) = cos M, cos (90° – M) = sin M;

7) tan (90° – M) = cot M, cot (90° – M) = tan M

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1. What are the basics of trigonometry?

The basic of trigonometry are –

NAME |
ABBREVIATION |
RELATIONSHIP |

Sine |
Sin |
Sin (θ)= Opposite/Hypotenuse |

Cosine |
Cos |
Cos (θ)= Adjacent/Hypotenuse |

Tangent |
Tan |
Tan (θ)= Opposite/Adjacent |

Cosecant |
Cosec |
Cosec ( θ)= Hypotenuse/Opposite |

Secant |
Sec |
Sec ( θ) = Hypotenuse/Adjacent |

Cotangent |
Cot |
Cot ( θ) = Adjacent/ Opposite |

2. What do you mean by trigonometry?

- As the name suggests, trigonometry is all about triangles.
- To be more specific, it is more about right-angled triangles, the triangles with one angle equal to 90 degrees.
- It is a system that helps us to find missing angles and missing sides of a triangle.
- The word "trigono" generally means triangle and the word "metry" denotes measure.

3. Explain the terms sin cos and tan?

The terms sin, cos, and tan can be defined by the following table -

NAME |
ABBREVIATION |
RELATIONSHIP |

Sine |
Sin |
Sin (θ)= Opposite/Hypotenuse |

Cosine |
Cos |
Cos (θ)= Adjacent/Hypotenuse |

Tangent |
Tan |
Tan (θ)= Opposite/Adjacent |

4. Who is the father of trigonometry?

The first trigonometric table was apparently compiled by Hipparchus in (180-125 BCE), who is now known as "the father of trigonometry”. He was the first to tabulate the corresponding values of arc and chord for a series of angles.