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NCERT Solutions for Class 10 Maths Chapter 8 Introduction to Trigonometry

NCERT Solutions for Class 10 Maths Chapter 8 Introduction to Trigonometry will help you quickly understand the concepts of the chapter. Trigonometry is introduced for the first time in Class 10. So you must study this chapter thoroughly as it will affect your learning in higher classes. The NCERT Solutions that the askIITians experts have created help you achieve this goal. We have included comprehensive explanations, stepwise solutions, and easy to understand methodologies so that you can prepare this chapter well for Class 10 Maths board exams. These NCERT Solutions are free to download. You can refer to them at any time and study at your own pace. 

About NCERT Class 10 Maths Chapter 8 Introduction to Trigonometry 

 

The Trigonometry chapter introduces you to the concepts of trigonometric ratios, trigonometric ratios of specific angles, trigonometric ratios of complementary angles, and trigonometric identities. Trigonometry is an important topic from the board exams as well as competitive exams like JEE and NEET. You must solve all the exercise questions of the chapter carefully.

Important points related to NCERT Class 10 Maths Chapter 8 Introduction to Trigonometry: 

Trigonometric Ratios: Ratios of the sides of a right triangle with respect to its acute angles are called trigonometric ratios of the angle.

Trigonometric ratios are given as:

Sine = length of the leg opposite to the anglelength of the hypotenuse

Cosine = length of the leg adjacent to the anglelength of the hypotenuse

Tangent =  length of the leg opposite to the anglelength of the leg adjacent to the angle

Secant = length of the hypotenuselength of the leg adjacent to the angle

Cosecant = length of the hypotenuselength of the leg opposite to the angle

Secant = length of the leg adjacent to the anglelength of the leg opposite to the angle

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.

Trigonometric Ratios of Specific Angles: Trigonometric ratios of angles of 30°, 45°, 60° and 90° are given as: 

Sin 45° = side opposite to angle 45°hypotenuse

Cos 45° = side adjacent to angle 45°hypotenuse

Tan 45° = side opposite to angle 45°side adjacent to angle 45° 

Cosec 45° = 1Sin 45°

Sec 45° = 1Cos 45°

Cot 45° = 1Tan 45°

In a similar way, we can find the trigonometric ratios angles of 30°, 60° and 90°. The following table gives the values of the trigonometric ratios of specific angles. You must learn how to draw this table as it will help you in solving questions in the exam:   

Complementary Angles: Two angles are called complementary angles if their sum is 90 degrees. So, to represent the complementary angle of an angle θ° we write it as (90-θ)°. 

Trigonometric ratios of Complementary Angles are given as:

  • Sin (90° – A) = cos A
  • Cos (90° – A) = sin A
  • Tan (90° – A) = cot A
  • Cot (90° – A) = tan A
  • Sec (90° – A) = cosec A
  • Cosec (90° – A) = sec A

Trigonometric Identities: When we calculate the trigonometric ratios for some specific angles and establish some identities involving these ratios, those identities are called trigonometric identities. Three important trigonometric identities are:

  • sin2 A + cos2 A = 1 
  • sec2 A – tan2 A = 1 for 0° ≤ A < 90° 
  • cosec2 A = 1 + cot2 A for 0° < A ≤ 90º

Download Free NCERT Solutions for Class 10 Maths Chapter 8 Introduction to Trigonometry

Students often find trigonometry difficult as it is a new topic for them. They need some guidance to solve the NCERT exercise questions which is why we have created exercise-wise NCERT Solutions. Let us see what is included in each exercise of the trigonometry chapter. 

 

NCERT Solutions for Class 10 Maths Chapter 8 Ex 8.1 

The first exercise of the trigonometry chapter is based on trigonometric ratios. There are 11 questions in this exercise in which you have to calculate the trigonometric ratios for sin, cos, tan, cot, sec, and cosec. The exercise includes very short question answers and short question answers. Check our NCERT Solutions for Class 10 Maths Chapter 8 Introduction to Trigonometry Ex 8.1 and learn how to solve the questions of this exercise step by step. 

 

NCERT Solutions for Class 10 Maths Chapter 8 Ex 8.2 

The second exercise of the trigonometry chapter is based on trigonometric ratios of specific angles of 30°, 45°, 60° and 90°. There are 4 questions in this exercise and all of them are important from the exam perspective. This exercise also includes multiple-choice questions (MCQs) which will test your understanding of the concepts of trigonometric ratios of specific angles. 

 

NCERT Solutions for Class 10 Maths Chapter 8 Ex 8.3 

The third exercise of the trigonometry chapter is based on trigonometric ratios of complementary angles. There are 7 questions in this exercise. We have provided stepwise solutions for all of them. Our easy to understand explanations will help you understand the concept of this exercise clearly. 

 

NCERT Solutions for Class 10 Maths Chapter 8 Ex 8.4 

The fourth exercise of this chapter is based on trigonometric identities. This is an important exercise from the perspective of the Class 10 CBSE board examination. You must practice all the questions of this exercise carefully. There are 5 questions in this exercise and many questions have different sub-parts so that you practise the trigonometric identities thoroughly. 

 

Important features of NCERT Solutions for Class 10 Maths Chapter 8:

  • The NCERT Solutions are prepared by experienced teachers at askIITians. 
  • The solutions are free of cost and can be downloaded as PDFs. 
  • We have organised the solutions of the chapter exercise-wise for your ease. 
  • The solutions include stepwise answers and easy to understand explanations. 
  • You can study these solutions at your own pace and learn independently. 

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

  1. How many questions are there in Class 10 Maths Chapter 8 Trigonometry? 

There are 4 exercises and 27 questions in the Introduction to Trigonometry chapter of Class 10 Maths. 

  1. Are all the exercises of the Introduction to Trigonometry chapter important? 

Yes, every exercise in the trigonometry chapter is important for you. This chapter enhances your fundamental understanding of trigonometry so you must practice all the exercise questions given in this chapter. 

  1. Do you provide extra questions for the trigonometry chapter? 

Yes, you can find important questions and extra questions for the trigonometry chapter on the askIITians website. 


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