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

Our comprehensive** **NCERT Solutions for Class 10 Maths Chapter 8 – Introduction to Trigonometry** **not only enables you to ace CBSE Class 10 board exams but also prepares you conceptually for various competitive exams. They have been carefully prepared by a renowned Maths teacher on the basis of the latest CBSE Class 10 Maths Syllabus. Some of the important topics covered in this chapter include trigonometric ratios, trigonometric ratios of some specific angles, trigonometric ratios of complementary angles, and trigonometric identities.

Introduction to Trigonometry covers the topics given in CBSE NCERT Solutions for Class 10 Maths book. They keep your concepts clear and help you develop a strong conceptual foundation. They are just what you need for quick and effective learning and revision of the topics covered in this chapter during your board exams. They follow a logical flow and answer all questions of all exercises in a step by step manner to help you understand all significant concepts covered in this chapter easily.

Maths Chapter 8 – Introduction to Trigonometry also provides you with the best tips and methods to understand and remember different formulas and identities explained in this chapter. They have been specifically devised to make learning fun, interesting and a highly productive process. Our Class 10 Maths Introduction to Trigonometry solutions give you a good amount of practice to grasp all topics easily. They cover all possible question types that can be asked in your board exams from this unit.

## NCERT Class 10 Maths Chapter 8: Important Topics

**Introduction**

This chapter of CBSE NCERT Solutions for Class 10 Maths Chapter 8 introduces you to a specialized branch of mathematics, called Trigonometry, which is used to measure heights/lengths of bigger objects and distances which otherwise are difficult to measure. Trigonometry is about learning of relationships between the sides and angles of a triangle. This chapter teaches you that ratios of the sides of a right triangle with respect to its acute angles are called trigonometric ratios of the angle.

**Trigonometric Ratios**

The 8th chapter of CBSE NCERT Class 10 Maths Book teaches you that the trigonometric ratios of an acute angle inside a right triangle tell the relationship among the angle and the length of its sides. Consider the triangle ABC right angled at B. These ratios are always defined with respect to acute angle ‘A’ or ‘C’. The angle can also be depicted through ‘θ’.

First, we identify the angle with respect to which the trigonometric ratios are to be calculated, and once we have recognized the sides, we can define 6 trigonometric ratios with respect to the sides –

sin A = side opposite to angle A/ hypotenuse

cos A = side adjacent to angle/ hypotenuse

tan A = side opposite to angle A/side adjacent to angle A.

cosec A = 1/sin A; sec A = 1 / cos A; tan A = 1/ cot A; tan A = sin A/ cos A

The symbol sin A is used as shortening for ‘the sine of the angle A’ not sin multiplied by A. When we know one of the trigonometric ratios of an acute angle, we can determine the remaining trigonometric ratios of the angle. The values related to trigonometric ratios of an angle remain unchanged upon changing the lengths of the sides of the triangle, provided the angle remains the same.

**Trigonometric Ratios of Some Specific Angles**

This portion of Class 10 Maths Introduction to Trigonometry derives the specific numerical values for trigonometric ratios for 0°, 30°, 45°, 60° and 90°. It can be observed that as ∠ A increases from 0° to 90°, sin A increases from 0 to 1 whereas cos A decreases from 1 to 0. This is because the adjacent side can never be greater than the hypotenuse as it is the longest side of a right-angle triangle.

**Trigonometric Ratios of Complementary Angles**

This part of the chapter teaches you that two angles are said to be complementary if their sum equals 90°. In a right-angled triangle, the other two angles than the right angle, have the sum of 90° and hence are complementary. Hence, 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; for all the values of angle A lying between 0° and 90°.

**Trigonometric Identities**This part of the NCERT Class 10 Maths Chapter 8 – Introduction to Trigonometry teaches you that an equation involving trigonometric ratios of an angle is called a trigonometric identity. The trigonometric identities are –

sin^{2} A + cos^{2}A = 1,

sec^{2}A – tan^{2}A = 1 for 0° ≤ A < 90°,

cosec^{2}A = 1 + cot^{2} A for 0° < A ≤ 90º

### NCERT CBSE Class 10 Maths Chapter 8 Exercise-Discussion

CBSE NCERT Class 10 Maths Chapter 8 consists of 4 exercises. NCERT Solutions for Class 10 Maths Chapter 8 – Introduction to Trigonometry provides you with the methodical solutions of all the questions asked in all the exercises. Here is a list of the exercises and their components-

**Exercise 8.1 **

This exercise of NCERT Class 10 Maths Chapter 8 has 11 questions. Questions 1, 2 and 10 ask you to find different trigonometric ratios for a given right angle triangle. Questions 3, 4 and 5 ask you to find some trigonometric ratios using the information given. Questions 6 to 9 ask you to derive and prove relations between trigonometric ratios for a particular system. Question 11 asks you to tell whether the statements given are true or false based on the concepts learnt.

**Exercise 8.2 **

This exercise of NCERT CBSE Class 10 Maths Chapter 8 has 4 questions. Question 1 asks you to evaluate 5 different expressions containing trigonometric ratios of special angles. Question 2 has four multiple-choice questions based on different expressions containing trigonometric ratios of special angles. Question 3 asks you to find values of angles A and B when values of tan(A+B) and tan(A-B) are given. Question 4 asks you to tell whether the statements given are true or false based on the concepts learnt in this chapter.

**Exercise 8.3 **

This exercise of NCERT CBSE Class 10 Maths Chapter 8 has 7 questions. Question 1 asks you to evaluate ratios for complementary angles. Questions 2, 4, 6 and 7 ask you to find the values of angles when certain expressions relating the trigonometric ratios are given. Question 3 and 5 ask you to calculate the value of angle A when expressions relating trigonometric ratios are given.

**Exercise 8.4 **

This exercise has 5 questions. Questions 1 and 2 ask you to create trigonometric identities. Questions 3 and 4 ask you to evaluate a few different identities given and answer accordingly. Questions 5 has 10 parts, and all of them ask you to prove the trigonometric identities given for acute angles.

NCERT Solutions for Class 10 Maths Chapter 8 – Introduction to Trigonometry provides accurate answers to the questions of above exercises given in NCERT Class 10 Maths Chapter 8 and they have been prepared using the best methods of solving and describing these questions.