NCERT Solutions for Class 10 Maths Chapter 8 Introduction to Trigonometry

 

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

This chapter introduces the concept of trigonometry. We will study some ratios of a right-angled triangle with respect to its acute angles, and this ratio called trigonometric ratios of the angles. Unit 5 "Trigonometry" holds 12 marks out of 80 marks in the maths paper of class 10 CBSE exam. And we can expect 2-3 question from this chapter of total around 8 marks. This chapter contain4 exercises with 27 questions. The NCERT Solutions for Class 10 Maths Chapter 8 Introduction to Trigonometry are solved by our subject experts to help students in their preparation of CBSE Class 10 Board exam. These NCERT solutions are the detailed explanation of each question of class 10 NCERT maths textbook.

In all the situations where the right angle triangle can be imagined, the heights or distances can be found by using some mathematical approach, which comes under a branch of mathematics called ‘trigonometry’. The trigonometry is the study of relationships between angles and the sides of a triangle. The NCERT Class 10 Maths Chapter 8 Introduction to Trigonometry also defines the trigonometric ratios for angles of measure 0^oand 90^o. We will also learn how to calculate the trigonometric identities and solve some specific angles of the trigonometric ratios cosine, sine, tangents etc. If any trigonometric ratio of an acute angle is known, the remaining trigonometric ratios of an angle can be easily determined.   

The trigonometric ratios of the angle A in right triangle ABC are defined as follows-

The trigonometric ratios

\\sine \:of\: \angle A=\frac{side \:opposite \:to \:angle \:A}{hypotenuse}=\frac{BC}{AC}\\\\cosine \:of\: \angle A=\frac{side \:adjacent\: to \:angle \:A}{hypotenuse}=\frac{AB}{AC}\\\\tangent \:of\: \angle A=\frac{side \:opposite \:to \:angle \:A}{side \:adjacent\: to \:angle \:A}=\frac{BC}{AB}\\\\cosecant \:of\:\angle A=\frac{hypotenuse}{side \:opposite \:to \:angle \:A}=\frac{AC}{BC}\\\\secant \:of \:\angle A= \frac{hypotenuse}{side \:adjacent\: to \:angle \:A}=\frac{AC}{AB}\\\\cotangent \:of\: \angle A=\frac{side \:adjacent\: to \:angle \:A}{side \:opposite \:to \:angle \:A}=\frac{AB}{BC}

The values of all the trigonometric ratios of 0°, 30°, 45°, 60°, and 90° are-

   \angle A     0^o    30^o       45^o    60^o   90^o

Sin A

  0    \frac{1}{2}   \frac{1}{\sqrt{2}}   \frac{\sqrt{3}}{2}  

1

Cos A

1   \frac{\sqrt{3}}{2}   \frac{1}{\sqrt{2}}        \frac{1}{2}    

0

Tan A

 0   \frac{1}{\sqrt{3}} 1   \sqrt{3}

 Not defined

Cosec A

 Not defined  2 \sqrt{2}   \frac{2}{\sqrt{3}}

1

Sec A  

  1   \frac{2}{\sqrt{3}}   \sqrt{2}    2

 Not defined

Cot A

 Not defined   \sqrt{3}    1   \frac{1}{\sqrt{3}}

 0

Topics of NCERT Grade 10 Maths Chapter 8 Introduction to Trigonometry-

8.1 Introduction

8.2 Trigonometric Ratios     

8.3 Trigonometric Ratios of Some Specific Angles

8.4 Trigonometric Ratios of Complementary Angles

8.5 Trigonometric Identities

8.6 Summary

The Complete Solutions of NCERT Class 10 Mathematics Chapter 8 is provided below:

NCERT Solutions for Class 10 Maths Chapter  8 Introduction to Trigonometry - Exercise 8.1

NCERT Solutions for Class 10 Maths Chapter  8 Introduction to Trigonometry - Exercise 8.2

NCERT Solutions for Class 10 Maths Chapter  8 Introduction to Trigonometry - Exercise 8.3

NCERT Solutions for Class 10 Maths Chapter  8 Introduction to Trigonometry - Exercise 8.4

 

NCERT Solutions for Class 10 Maths - Chapter-wise

Chapter No.

Chapter Name

Chapter 1

Real Numbers

Chapter 2

Polynomials

Chapter 3

Pair of Linear Equations in Two Variables

Chapter 4

Quadratic Equations

Chapter 5

Arithmetic Progressions

Chapter 6

Triangles

Chapter 7

Coordinate Geometry

Chapter 9

Some Applications of Trigonometry

Chapter 10

Circles

Chapter 11

Constructions

Chapter 12

Areas Related to Circles

Chapter 13

Surface Areas and Volumes

Chapter 14

Statistics

Chapter 15

Probability

 

NCERT Solutions for Class 10 - Subject Wise

NCERT Solutions for Class 10 Maths

NCERT Solutions for Class 10 Science

 

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