introduction to trigonometry class 10 assignment

NCERT Solutions for Class 10 Maths Chapter 8 Introduction to Trigonometry

Get here the NCERT Solutions for class 10 Maths Chapter 8 Introduction to Trigonometry in English and Hindi Medium for session 2024-25. The solution of chapter 8 class 10th Maths is modified and revised as per the new textbooks published by NCERT for academic year 2024-25.

Class 10 Maths Chapter 8 Exercise 8.1 Solutions

• Class 10th Maths Exercise 8.1 in English
• Class 10th Maths Exercise 8.1 in Hindi

Class 10 Maths Chapter 8 Exercise 8.2 Solutions

• Class 10th Maths Exercise 8.2 in English
• Class 10th Maths Exercise 8.2 in Hindi

Class 10 Maths Chapter 8 Exercise 8.3 Solutions

• Class 10th Maths Exercise 8.3 in English
• Class 10th Maths Exercise 8.3 in Hindi

10th Maths Chapter 8 Solutions for State Boards

• Class 10 Maths Chapter 8 Exercise 8.1
• Class 10 Maths Chapter 8 Exercise 8.2
• Class 10 Maths Chapter 8 Exercise 8.3
• Class 10 Maths Chapter 8 Exercise 8.4
• Class 10 Maths Solutions Page
• Class 10th all Subjects NCERT Solutions

All the contents are updated for new academic session 2024-25 based on latest NCERT Books. UP Board students are also using NCERT Textbooks for their exams now. So, they also can download UP Board Solutions for Class 10 Maths Chapter 8 Solutions in Hindi Medium from this page. Solutions are given in videos format also describing in English and Hindi.

NCERT Solutions and Offline apps for UP Board and CBSE Board are also given free to download. Download Offline as well as Online Apps based on updated NCERT Solutions based on latest NCERT books 2024-25. Revision books are also available to download. Description, history and identities related to Trigonometry is given below.

NCERT Solutions for class 10 Maths Chapter 8 Introduction to Trigonometry exercises from 8.1 to 8.3 are given to use online of download in PDF format free. These solutions are in Hindi and English Medium format. If you have any doubt, please visit to Discussion Forum to ask your doubts.

1. The creator of trigonometry is said to have been the Greek Mathematician Hipparchus of the 2nd century BC. 2. The word Trigonometry which means triangle measurement is credited to Bastholoman Pitiscus (1561-1613). 3. The first use of the idea of ‘sine’ can be found in the work of ‘Aryabhatiyam’ of Aryabhata in 500 AD. Aryabhata used the word Ardha-jya for the half-chord, which was shortened to Jya or Jiva in due course. When the Aryabhatiyam was translated into Arabic, the word Jiva was retained. It was further translated into ‘Sinus’, which means curve in Latin. The word ‘Sinus’ also used as sine was first abbreviated and used as ‘sin’ by an English professor of astronomy Edmund Gunter (1581-1626). 4. The origin of the terms ‘Cosine’ and ‘tangent’ was much later. The cosine function arose from the need to compute the sine of the complementary angle. Aryabhata called it Kotijya. The name cosinus originated with Edmund Gunter. In 1674, another English mathematician Sir Jonas Moore first used the abbreviated notation ‘cos’.

How many exercise wise questions are there in class 10 Maths chapter 8?

There are 4 exercises in class 10 math chapter 8 Introduction to Trigonometry. In first exercise (Ex 8.1), there are in all 11 questions. In second exercise (Ex 8.2), there are in all 4 questions. In third exercise (Ex 8.3), there are 5 questions. So, there are in all 20 questions in class 10 math chapter 8 Introduction to Trigonometry. There are in all 15 examples in class 10 math chapter 8 Introduction to Trigonometry. Examples 1, 2, 3, 4, 5 are based on Ex 8.1. Examples 6, 7, 8 are based on Ex 8.2. Examples 12, 13, 14, 15 are based on Ex 8.3.

What are the important examples from chapter 8 class 10 math?

Examples given in NCERT books are always important for CBSE exams. Examples 3, 4, 5, 7, 8, 10, 11, 13, 14 and 15 of chapter 8 (Introduction to Trigonometry) of class 10 math are the important examples from exam point of view. In exam questions can come from these examples.

Which are the main topics students go through in chapter 8 of class 10th Mathematics?

In chapter 8 Introduction to Trigonometry of class 10th math, Students will study: 1) Trigonometric Ratios. 2) Trigonometric Ratios of Some Specific Angles. 3) Trigonometric Identities. This chapter is very interesting. Also this chapter is completely new for students.

Why is chapter 8 of Class 10th Maths important?

Chapter 8 (Introduction to Trigonometry) of 10th Math is important because there is a chapter in class 11th math named Trigonometric functions and chapter 8 (Introduction to Trigonometry) of 10th Math works as a base for that chapter. Also from exam point of view chapter 8 (Introduction to Trigonometry) of 10th Math is very important. Every year 7-8 marks questions come from this chapter.

What do you learn about Trigonometry in Class 10 Maths Chapter 8?

Trigonometry is the oldest branch of mathematics. This concept was first used by Aryabhata in Aryabhatiyam in 500 A.D. Trigonometry is a word consisting of three Greek words: Tri-Gon-Metron. ‘Tri’ means three, ‘Gon’ means side and ‘Metron’ means measure. So, trigonometry is the study related to the measure of sides and angles of a triangle in particular, right triangles (in CBSE class 10).

How can I score more that 90% in class 10 Maths Chpater 8 Trigonometry?

To score well in trigonometry, we should practice hard the entire chapter 8 in 10th Maths. Specially exercise 8.4 needs more time to spend for solving the questions based on identities. All the parts of question 5 of exercise 8.4 asked in exams frequently.

Is there any application of trigo as a tool in astronomy for Class 10 Mathematics 8th Chapter?

Trigonometry is used in astronomy to determine the position and the path of celestial objects. Astronomers use it to find the distance of the stars and planets from the Earth. Captain of a ship uses it to find the direction and the distance of islands and light houses from the sea. Surveyors use to map the new lands.

What is the objective of Chapter 8 in Class 10 Maths Trigonometry?

Objective of Class 10 Trigonometry: Identifying the opposite side, adjacent side and hypotenuse of right triangle with respect to given angle A. Defining the six rations (sine, cosine, tangent, secant. cosecant and cotangent) related to the sides of a right angled triangle. Finding the values of trigonometric rations of a given right angled triangle. Finding the values of trigonometry rations of some standard angles (0, 30, 45, 60 and 90) in degrees. Using complementary angles and applying it into trigonometric identities to prove another identities.

« Chapter 7: Coordinate Geometry

Chapter 9: some applications of trigonometry ».

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Chapter 8 Class 10 Introduction to Trignometry

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The chapter is updated according to the new NCERT, for 2023-2024 Board Exams.

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Trigonometry means studying relationship between measures of triangle. Usually, we talk about right triangles when we study trigonometry,

In this chapter, we will study

• What is sin, cos, tan ( Sine, cosine, tangent) ... and how they are found in a triangle
• What is sec, cosec, cot, and how is it related to sin, cos, tan.
• (Sin, cos, tan, sec, cosec, cot are known as Trigonometric Ratios)
• Then, we study Trigonometric ratios of specific angles l ike 0°, 30°, 45°, 60°, 90° ; and do some questions
• We study the formulas of sin (90 - θ) , cos (90 - θ), tan (90 - θ)
• And then we study Trigonometric Identities, and how other identities are derived from sin 2 θ + cos 2 θ = 1

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NCERT Solutions Class 10 Maths Chapter 8 Introduction to Trigonometry

NCERT solutions for class 10 maths chapter 8 Introduction to Trigonometry builds on the concept of a right triangle and introduces students to the basics of trigonometry. The word ‘trigonometry’ is derived from the Greek words ‘tri’ (meaning three), ‘gon’ (meaning sides), and ‘metron’ (meaning measure). Trigonometry can be defined as the study of relationships between the sides and angles of a triangle. There are two main concepts that students will learn in this chapter, which are, trigonometric ratios and trigonometric identities. Most of the technologically advanced methods used in Engineering and Physical Sciences are based on trigonometric concepts making it an extremely important lesson. This is one of the most scoring topics in the board examinations provided they go through the topic with diligence and in an organized manner. These concepts are also used in sister topics of higher classes such as calculus and geometry.

NCERT solutions class 10 maths Chapter 8 helps students recognize the trigonometric functions that are used in an equation. There are 6 trigonometric ratios in a right-angled triangle. These are sine , cosine , tangent , cosecant , secant, and cotangent. These solutions will be the perfect guidelines that a student can use to build a very strong conceptual foundation of these ratios. They also enable kids to explore some practical applications of trigonometry. In this class 10 maths NCERT solutions Chapter 8, we will take a look at this lesson in detail and see how to effectively apply these concepts and also you can find some of these in the exercises given below.

• NCERT Solutions Class 10 Maths Chapter 8 Ex 8.1
• NCERT Solutions Class 10 Maths Chapter 8 Ex 8.2
• NCERT Solutions Class 10 Maths Chapter 8 Ex 8.3
• NCERT Solutions Class 10 Maths Chapter 8 Ex 8.4

NCERT Solutions for Class 10 Maths Chapter 8 PDF

A trigonometric ratio of an acute angle in a right triangle expresses the relationship between the angle and the length of its sides. The entire chapter of trigonometry is based on this simple concept. Throughout this lesson, there will be several important inferences drawn from theorems that will be useful in performing calculations. One such fact is that the values of the trigonometric ratios of an angle do not vary with the lengths of the sides of the triangle if the angle remains the same. To learn more, the NCERT solutions class 10 maths chapter 8 Introduction to Trigonometry can be downloaded for free in a scrollable PDF format using the links given below.

☛ Download Class 10 Maths NCERT Solutions Chapter 8

NCERT Class 10 Maths Chapter 8   Download PDF

NCERT Solutions for Class 10 Maths Chapter 8

NCERT Solutions Class 10 Maths Chapter 8 Introduction to Trigonometry covers all the basic concepts of trigonometry. This chapter also consists of many interesting formulas that can help solve questions related to real-life situations. Trigonometry is an essential concept for higher classes and competitive exams. As this is such a crucial lesson it is highly recommended to revise the important concepts outlined regularly. You can go through the detailed analysis of NCERT Solutions Class 10 Maths Chapter 8 Introduction to Trigonometry mentioned below:

• Class 10 Maths Chapter 8 Ex 8.1 - 11 Questions
• Class 10 Maths Chapter 8 Ex 8.2 - 4 Questions
• Class 10 Maths Chapter 8 Ex 8.3 - 7 Questions
• Class 10 Maths Chapter 8 Ex 8.4 - 5 Questions

☛ Download Class 10 Maths Chapter 8 NCERT Book

Topics Covered: The topics covered in class 10 maths NCERT Solutions chapter 8 are trigonometric ratios , trigonometric identities , trigonometric ratios of specific angles , and trigonometric ratios of complementary angles . The discussion on trigonometric ratio and identities will be limited to acute angles only.

Total Questions: Class 10 maths chapter 8 Introduction to Trigonometry consists of 27 questions, of which 10 are straightforward, 10 are moderate, and 7 are long answer type problems. These sums have been distributed over 4 exercises.

List of Formulas in NCERT Solutions Class 10 Maths Chapter 8

NCERT Solutions Class 10 Maths Chapter 8 is a chapter based on formulas. It is advisable to create a formula chart as there are several formulas associated with trigonometry . Students must memorize all these formulas in order to produce satisfactory results and solve problems. As it can get confusing at times hence, practicing sums based on these formulas and identities is equally necessary. Kids can also go through the derivation of these formulas to develop a rock-solid foundation as well as understand the underlying concepts. Let us now go through some of the formulas covered in this chapter.

• sin A = Perpendicular/ Hypotenuse
• cos A = Base/ Hypotenuse
• tan A = Perpendicular/ Base
• cos 2 A + sin 2 A = 1
• 1 + tan 2 A = sec 2 A
• cot 2 A + 1 = cosec 2 A

Important Questions for Class 10 Maths NCERT Solutions Chapter 8

Video solutions for class 10 maths ncert chapter 8, faqs on ncert solutions class 10 maths chapter 8, why are ncert solutions class 10 maths chapter 8 important.

NCERT solutions class 10 maths chapter 8 will help students establish a relationship between the sides and angle of a triangle. This topic is important for class 10 maths as it carries a huge weightage in exams and is very scoring. Chapter 8 lays a foundation for more complex trigonometry topics that will be taught in higher classes. This is considered to be the most essential subject matter that kids will be introduced to throughout their academic careers.

Do I Need to Practice all Questions Given in NCERT Solutions Class 10 Maths Introduction to Trigonometry?

Students should not miss out on any questions from NCERT Solutions Class 10 Maths Introduction to Trigonometry because each allows them to understand the topic at length and explore the formulas. A majority of questions are based on real-life examples thus, this topic becomes relatable and engaging. With the help of these problems, kids have the opportunity to score excellent results in their examinations.

What are the Important Topics Covered in NCERT Solutions Class 10 Maths Chapter 8?

The NCERT Solutions Class 10 Maths Chapter 8 have a set of topics that give kids a holistic understanding of this lesson hence, all are equally important. Students must progress through this chapter very meticulously and with great focus. There are several tips and tricks outlined in this lesson that are helpful not only in acing the board exams but also in attempting challenging problems that appear in higher classes.

How many questions are there in Class 10 Maths NCERT Solutions Chapter 8?

A total of 27 questions are included in NCERT solutions class 10 Maths Chapter 8 divided amongst 4 exercises. These sums cover different aspects of trigonometry including trigonometric ratios and identities. It is advisable for students to go through the chapter summary and solved examples before attempting these exercises.

What are the Important Formulas in NCERT Solutions Class 10 Maths Chapter 8?

One can find a variety of formulas in NCERT Solutions Class 10 Maths Chapter 8. Some of the important formulas are reciprocal functions, trigonometric ratios of complementary angles, the value of sin, cos, and many more. One has to master the formulas in order to crack all the questions of this chapter. Students can make formula charts to remember all the important formulas and revise them when required.

How can CBSE Students utilize NCERT Solutions Class 10 Maths Chapter 8 effectively?

CBSE students can utilize NCERT solutions class 10 maths chapter 8 effectively by solving each and every question. In case they get stuck on any problem, kids must check the detailed solutions to that sum. They can also go through the derivation of certain formulas to get a better idea of how to apply them to problems efficiently. It is necessary to go through all the theories before attempting the sums in order to get the most out of these solutions.

NCERT Solutions for Class 10 Maths Ch 8 Introduction to Trigonometry

NCERT Solutions for Class 10 Maths Chapter 8 Introduction to Trigonometry 

• Exercise 8.1
• Exercise 8.2
• Exercise 8.3
• Exercise 8.4

How many exercises in Chapter 8 Introduction to Trigonometry

If tan a = cot b, prove that a + b = 90°., what is the value of sinθ. cos(90° − θ) + cosθ . sin(90° − θ), express sin 67° + cos 75° in terms of ratios of angles between 0° and 45°., contact form.

CBSE NCERT Solutions

NCERT and CBSE Solutions for free

Class 10 Mathematics Trigonometry Assignments

We have provided below free printable Class 10 Mathematics Trigonometry Assignments for Download in PDF. The Assignments have been designed based on the latest NCERT Book for Class 10 Mathematics Trigonometry . These Assignments for Grade 10 Mathematics Trigonometry cover all important topics which can come in your standard 10 tests and examinations. Free printable Assignments for CBSE Class 10 Mathematics Trigonometry , school and class assignments, and practice test papers have been designed by our highly experienced class 10 faculty. You can free download CBSE NCERT printable Assignments for Mathematics Trigonometry Class 10 with solutions and answers. All Assignments and test sheets have been prepared by expert teachers as per the latest Syllabus in Mathematics Trigonometry Class 10. Students can click on the links below and download all Pdf Assignments for Mathematics Trigonometry class 10 for free. All latest Kendriya Vidyalaya Class 10 Mathematics Trigonometry Assignments with Answers and test papers are given below.

Mathematics Trigonometry Class 10 Assignments Pdf Download

We have provided below the biggest collection of free CBSE NCERT KVS Assignments for Class 10 Mathematics Trigonometry . Students and teachers can download and save all free Mathematics Trigonometry assignments in Pdf for grade 10th. Our expert faculty have covered Class 10 important questions and answers for Mathematics Trigonometry as per the latest syllabus for the current academic year. All test papers and question banks for Class 10 Mathematics Trigonometry and CBSE Assignments for Mathematics Trigonometry Class 10 will be really helpful for standard 10th students to prepare for the class tests and school examinations. Class 10th students can easily free download in Pdf all printable practice worksheets given below.

Topicwise Assignments for Class 10 Mathematics Trigonometry Download in Pdf

Advantages of Class 10 Mathematics Trigonometry Assignments

• As we have the best and largest collection of Mathematics Trigonometry assignments for Grade 10, you will be able to easily get full list of solved important questions which can come in your examinations.
• Students will be able to go through all important and critical topics given in your CBSE Mathematics Trigonometry textbooks for Class 10 .
• All Mathematics Trigonometry assignments for Class 10 have been designed with answers. Students should solve them yourself and then compare with the solutions provided by us.
• Class 10 Students studying in per CBSE, NCERT and KVS schools will be able to free download all Mathematics Trigonometry chapter wise worksheets and assignments for free in Pdf
• Class 10 Mathematics Trigonometry question bank will help to improve subject understanding which will help to get better rank in exams

Frequently Asked Questions by Class 10 Mathematics Trigonometry students

At https://www.cbsencertsolutions.com, we have provided the biggest database of free assignments for Mathematics Trigonometry Class 10 which you can download in Pdf

We provide here Standard 10 Mathematics Trigonometry chapter-wise assignments which can be easily downloaded in Pdf format for free.

You can click on the links above and get assignments for Mathematics Trigonometry in Grade 10, all topic-wise question banks with solutions have been provided here. You can click on the links to download in Pdf.

We have provided here topic-wise Mathematics Trigonometry Grade 10 question banks, revision notes and questions for all difficult topics, and other study material.

We have provided the best collection of question bank and practice tests for Class 10 for all subjects. You can download them all and use them offline without the internet.

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Trigonometry Formulas For Class 10

Trigonometry formulas for Class 10 are provided here for students. Trigonometry is the study of relationships between angles, lengths, and heights of triangles. It includes ratios, functions, identities, and formulas to solve problems based on it, especially for right-angled triangles.  Applications of trigonometry are also found in engineering, astronomy, Physics and architectural design. This chapter is very important as it comprises many topics like Linear Algebra, Calculus and Statistics.

Click here to Download the PDF of Trigonometry Formulas for Class 10:- Download PDF

Trigonometry is introduced in CBSE Class 10. It is a completely new and tricky chapter where one needs to learn all the formulas and apply them accordingly. Trigonometry Class 10 formulas are tabulated below.

List of Trigonometric Formulas for 10th Class

All the important formulas introduced to students in Class 10 are available here. Students can learn these formulas anytime from here and solve trigonometry-related problems.

The trigonometric formulas for ratios are majorly based on the three sides of a right-angled triangle, such as the adjacent side or base, perpendicular and hypotenuse (See the above figure).  Applying Pythagoras theorem for the given right-angled triangle, we have:

(Perpendicular) 2  + (Base) 2  = (Hypotenuse) 2

⇒ (P) 2  + (B) 2  = (H) 2

Now, let us see the formulas based on trigonometric ratios (sine, cosine, tangent, secant, cosecant and cotangent)

Basic Trigonometric formulas

The Trigonometric formulas are given below:

Reciprocal Relation Between Trigonometric Ratios

Trigonometric sign functions.

• sin (-θ) = − sin θ
• cos (−θ) = cos θ
• tan (−θ) = − tan θ
• cosec (−θ) = − cosec θ
• sec (−θ) = sec θ
• cot (−θ) = − cot θ

Trigonometric Identities

• sin 2 A + cos 2 A = 1
• tan 2 A + 1 = sec 2 A
• cot 2 A + 1 = cosec 2 A

Periodic Identities

• sin(2nπ + θ ) = sin θ
• cos(2nπ + θ ) = cos θ
• tan(2nπ + θ ) = tan θ
• cot(2nπ + θ ) = cot θ
• sec(2nπ + θ ) = sec θ
• cosec(2nπ + θ ) = cosec θ

Complementary Ratios

• sin(π/2 − θ) = cos θ
• cos(π/2 − θ) = sin θ
• tan(π/2 − θ) = cot θ
• cot(π/2 − θ) = tan θ
• sec(π/2 − θ) = cosec θ
• cosec(π/2 − θ) = sec θ

Quadrant II

• sin(π − θ) = sin θ
• cos(π − θ) = -cos θ
• tan(π − θ) = -tan θ
• cot(π − θ) = – cot θ
• sec(π − θ) = -sec θ
• cosec(π − θ) = cosec θ

Quadrant III

• sin(π + θ) = – sin θ
• cos(π + θ) = – cos θ
• tan(π + θ) = tan θ
• cot(π + θ) = cot θ
• sec(π + θ) = -sec θ
• cosec(π + θ) = -cosec θ

Quadrant IV

• sin(2π − θ) = – sin θ
• cos(2π − θ) = cos θ
• tan(2π − θ) = – tan θ
• cot(2π − θ) = – cot θ
• sec(2π − θ) = sec θ
• cosec(2π − θ) = -cosec θ

Sum and Difference of Two Angles

• sin (A + B) = sin A cos B + cos A sin B
• sin (A − B) = sin A cos B – cos A sin B
• cos (A + B) = cos A cos B – sin A sin B
• cos (A – B) = cos A cos B + sin A sin B
• tan ( A  +  B ) = [( tan  A  +  tan  B)/( 1  –  tan  A  tan  B)]
• tan ( A –  B ) = [( tan  A –   tan  B)/( 1 +   tan  A  tan  B)]

Double Angle Formulas

• sin 2A = 2 sin A cos A = [2 tan A /(1 + tan 2 A)]
• cos 2A = cos 2 A – sin 2 A = 1 – 2 sin 2 A = 2 cos 2 A – 1 = [(1 – tan 2 A)/(1 + tan 2 A)]
• tan 2A = (2 tan A)/(1 – tan 2 A)

Triple Angle Formulas

• sin 3A = 3 sinA – 4 sin 3 A
• cos 3A = 4 cos 3 A – 3 cos A
• tan 3A = [3 tan A – tan 3 A]/[1 − 3 tan 2 A]

Video Lesson on Trigonometry

More Formulas for Class 10

• Algebra Formulas For Class 10
• Geometry Formulas For Class 10
• Maths Formulas For Class 10
• Mensuration Formulas Class 10

Solved Examples

If sin A = ⅗, then find the value of cos A and cot A.

Using the identity, sin 2 A + cos 2 A = 1,

cos 2 A = 1 – (⅗) 2

= (25 – 9)/25

Considering only the positive part,

Also, cot A = cos A/sin A = (⅘)/(⅗) = 4/3

Evaluate sin 35° cos 55° + cos 35° sin 55°.

Given expression:

sin 35° cos 55° + cos 35° sin 55°

This is of the form sin A cos B + cos A sin B.

Thus, by using the identity sin(A + B) = sin A cos B + cos A sin B, we get;

sin 35° cos 55° + cos 35° sin 55° = sin(35° + 55°) = sin 90° = 1

If tan P = cot Q, then prove that P + Q = 90°.

tan P = cot Q

As we know, tan(90° – A) = cot A.

So, tan P = tan(90° – Q)

Therefore, P = 90° – Q

P + Q = 90°

Hence proved.

Practice Questions

• Evaluate: sin 28°/cos 62°
• Find the value of tan 1° tan 2° tan 3° … tan 89°.
• If cos A + cos 2 A = 1, then show that sin 2 A + sin 4 A = 1.

Frequently Asked Questions – FAQs

What are the six ratios of trigonometry, what are the pythagorean identities of trigonometry, how do you write the formulas for trigonometry ratios, what do you mean by complementary and supplementary angles, what is the maximum and minimum value of sinθ.

Put your understanding of this concept to test by answering a few MCQs. Click ‘Start Quiz’ to begin!

Select the correct answer and click on the “Finish” button Check your score and answers at the end of the quiz

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