NCERT Solutions of Class 10 Maths Chapter 8: Introduction to Trigonometry

Content Curator

NCERT Solutions of Class 10 Maths Chapter 8 Introduction to Trigonometry are given in the article. Trigonometry studies relationships between side lengths and angles of triangles. Chapter 8 Introduction to Trigonometry solutions cover key concepts such including Trigonometric ratios of an acute angle of a right-angled triangle & their proofs. Values of the trigonometric ratios of 30⁰, 40⁰, and 60⁰ and relationships between Ratios.

Class 10 Maths Chapter 8 Introduction to Trigonometry is a part of Unit 5 Trigonometry. This unit holds a weightage of 12 Marks in Class 10 Maths Examination 2022-23. NCERT Solutions of Class 10 Maths Chapter 8 are based on the following topics:

Download: NCERT Solutions for Class 12 Mathametics Chapter 8 pdf

NCERT Solutions of Class 10 Maths Chapter 8 Introduction to Trigonometry

NCERT Solutions of Class 10 Maths Chapter 8 Introduction to Trigonometry are provided below:

Also check: Introduction to Trigonometry

Important Topics: NCERT Solutions of 10 Maths Chapter 8 Introduction to Trigonometry

Important Topics of NCERT Solutions of 10 Maths Chapter 8 Introduction to Trigonometry are elaborated below:

Trigonometric Identities

There are 6 kinds of Trigonometric Idenities:

Sine
Cosine
Tangent
Secant
Cosecant
Cotangent

Example Prove the following identity using the trigonometric identities:

[(sin 3θ + cos 3θ)/(sin θ + cos θ)] + sin θ cos θ = 1

Solution: Let’s the following identity:

a³+b³ = (a+b)(a²-ab+b²)

Using Pythagoras Theorem,

L.H.S. = [(sin 3θ + cos 3θ)(sin θ + cos θ)] + sin θ cos θ

= [(sin θ + cos θ)(sin2θ - sin θ cos θ + cos2θ)(sin θ + cos θ) + sin θ cos θ

= (sin2θ - sin θ cos θ + cos2θ) + sin θ cos θ

= sin2θ + cos2θ = 1 = R.H.S.

Trigonometry Table

Trigonometry Table is a collection of values of trigonometric ratios for various standard angles including 0°, 30°, 45°, 60°, 90°, sometimes with other angles like 180°, 270°, and 360° included, in a tabular format.

Example: Calculate the exact value of sin15º using the trigonometric value for standard angles from a trigonometry table.

Solution: Using the trigonometric table, we know that sin45º = 1/√2, cos30º = (√3/2), cos45º = 1/√2, and sin30º = 1/2

sin15º = sin(45º - 30º) = sin45ºcos30º - cos45ºsin30º = (√2/2) • (√3/2) - (√2/2) • (1/2) = (√6 - √2)/4 = (√3 - 1)/2√2

Therefore, tThe value of sin15º = (√3 - 1)/2√2

Trigonometry Ratios

Trigonometric ratios are the “ratios of length of sides of a triangle”.

Trigonometric ratios relate the ratio of sides of a right triangle to the respective angle. Basic trigonometric ratios are sin, cos, and tan. Other important trigonometric ratios, cosec, sec, and cot, can be derived using the sin, cos, and tan respectively.

Sum, Difference, Product Trigonometric Ratios Identities

Sum, Difference, Product Trigonometric Ratios include the following formulas:

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)
cot (A + B) = (cot A cot B - 1)/(cot B - cot A)
cot (A - B) = (cot A cot B + 1)/(cot B - cot A)
2 sin A⋅cos B = sin(A + B) + sin(A - B)
2 cos A⋅cos B = cos(A + B) + cos(A - B)
2 sin A⋅sin B = cos(A - B) - cos(A + B)

NCERT Solutions For Class 10 Maths Chapter 8 Exercises

The detailed solutions for all the NCERT Solutions for Introduction to Trigonometry under different exercises are as follows:

Also check:

Important Chapter Related Topics
Introduction to Trigonometry Important Questions	Introduction to Trigonometry Formula	Introduction to trigonometry Revision Notes
Trigonometry Table	Cos 0	Value of cos 60
Sin 30 Degrees	sec 90	30 60 90 formula
cosec cot formula	sec 60	Difference between Trigonometry and Geometry

Also check:

Maths Study Guides
Math MCQs	Trigonometry	Mensuration
Geometry	Algebra	Difference Between in Maths
Maths Study Material	Math Formula	Class 10 Maths Study Notes

CBSE X Related Questions

1.
The following data shows the number of family members living in different bungalows of a locality:

Number of Members 0−2 2−4 4−6 6−8 8−10 Total
Number of Bungalows 10 p 60 q 5 120

If the median number of members is found to be 5, find the values of p and q.
View Solution
2.
A peacock sitting on the top of a tree of height 10 m observes a snake moving on the ground. If the snake is $10\sqrt{3}$ m away from the base of the tree, then angle of depression of the snake from the eye of the peacock is
- $60^\circ$
- $45^\circ$
- $30^\circ$
- $90^\circ$
View Solution
3.
Two identical cones are joined as shown in the figure. If radius of base is 4 cm and slant height of the cone is 6 cm, then height of the solid is
- 8 cm
- $4\sqrt{5}$ cm
- $2\sqrt{5}$ cm
- 12 cm
View Solution
4.
Find the mean and mode of the following data:
Class 15--20 20--25 25--30 30--35 35--40 40--45
Frequency 12 10 15 11 7 5
View Solution
5.
OAB is sector of a circle with centre O and radius 7 cm. If length of arc $ \widehat{AB} = \frac{22}{3} $ cm, then $ \angle AOB $ is equal to
- $ \left(\frac{120}{7}\right)^\circ $
- $ 45^\circ $
- $ 60^\circ $
- $ 30^\circ $
View Solution
6.
The number of red balls in a bag is three more than the number of black balls. If the probability of drawing a red ball at random from the given bag is $\dfrac{12}{23}$, find the total number of balls in the given bag.
View Solution

Number of Members	0−2	2−4	4−6	6−8	8−10	Total
Number of Bungalows	10	p	60	q	5	120

View All

Similar Mathematics Concepts

Trigonometry: Ratios, Identities & Trigonometric Table

Introduction to Trigonometry Formula: Ratios and Identities

Introduction to Trigonometry Important Questions: Applications of Trigonometry

Sin 30 Degrees: Value, Derivation & Trigonometry Table

Value of Cos 60 Degrees: Formula, Derivation, Examples

Introduction to Trigonometry Revision Notes

NCERT Solutions for Class 10 Maths: Chapter-wise Solutions and Important Topics

MCQs On Introduction to trigonometry: Introduction & Explanation

Difference Between Trigonometry and Geometry: Important Formulas

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

CBSE X Syllabus

Mathematics Preparation Guides

Arithmetic Progressions: Properties, Formulas and Solved Examples

Distance Formula and Derivation of Coordinate Geometry

Probability- A Theoretical Approach: An Overview and Examples

Area of Circle: Area Formula, Derivation with Solved Examples

Mode of Grouped Data

Pythagoras Theorem: Formula, Theorem, Proof and Examples

Nature of Roots of Quadratic Equation

Probability: Concepts, Problems and Solved Examples

Trigonometry: Ratios, Identities & Trigonometric Table

Heights and Distances: Applications in Trigonometry

Real Numbers: Euclid’s Division Lemma, Properties & Sets

Surface Areas and Volumes Revision Notes

Circles: Definition, Properties, Parts, Theorems

Constructions Revision Notes

Pair of Linear Equations In Two Variables Important Questions

Circles Revision Notes: Theorems of Tangent to the Circle

Statistics Important Questions

Mathematics NCERT Solutions

Euclid's Division Lemma: Proof, Finding HCF & Examples

Area of a Sector: Definition, Formulae and Solved Examples

Real Numbers: Definition, Properties and Examples

Events in Probability: Definition, Types, Examples

Relation Between HCF and LCM: Definition, Methods and Formulas

Geometric Probability: Formula, Illustration, Model

Algebra Formula: Important Formulas in Algebra & Solved Examples

Angle of Depression: Definition, Formula and Solved Examples

Cyclic Quadrilateral: Properties, Theorems and Formulas

Polynomial Notation: Types, Remainder Theorem, Linear and Quadratic Equation

You can also check

NCERT Solutions of Class 10 Maths Chapter 8: Introduction to Trigonometry

NCERT Solutions of Class 10 Maths Chapter 8 Introduction to Trigonometry

Important Topics: NCERT Solutions of 10 Maths Chapter 8 Introduction to Trigonometry

Trigonometric Identities

Trigonometry Table

Trigonometry Ratios

NCERT Solutions For Class 10 Maths Chapter 8 Exercises

CBSE X Related Questions

1.
The following data shows the number of family members living in different bungalows of a locality:

Number of Members 0−2 2−4 4−6 6−8 8−10 Total
Number of Bungalows 10 p 60 q 5 120

If the median number of members is found to be 5, find the values of p and q.

2.
A peacock sitting on the top of a tree of height 10 m observes a snake moving on the ground. If the snake is $10\sqrt{3}$ m away from the base of the tree, then angle of depression of the snake from the eye of the peacock is

3.
Two identical cones are joined as shown in the figure. If radius of base is 4 cm and slant height of the cone is 6 cm, then height of the solid is

4.
Find the mean and mode of the following data:
Class 15--20 20--25 25--30 30--35 35--40 40--45
Frequency 12 10 15 11 7 5

5.
OAB is sector of a circle with centre O and radius 7 cm. If length of arc \( \widehat{AB} = \frac{22}{3} \) cm, then \( \angle AOB \) is equal to

6.
The number of red balls in a bag is three more than the number of black balls. If the probability of drawing a red ball at random from the given bag is $\dfrac{12}{23}$, find the total number of balls in the given bag.

Similar Mathematics Concepts

Comments

SUBSCRIBE TO OUR NEWS LETTER

Class	15--20	20--25	25--30	30--35	35--40	40--45
Frequency	12	10	15	11	7	5

NCERT Solutions of Class 10 Maths Chapter 8: Introduction to Trigonometry

NCERT Solutions of Class 10 Maths Chapter 8 Introduction to Trigonometry

Important Topics: NCERT Solutions of 10 Maths Chapter 8 Introduction to Trigonometry

Trigonometric Identities

Trigonometry Table

Trigonometry Ratios

NCERT Solutions For Class 10 Maths Chapter 8 Exercises

CBSE X Related Questions

1.The following data shows the number of family members living in different bungalows of a locality: Number of Members0−22−44−66−88−10TotalNumber of Bungalows10p60q5120If the median number of members is found to be 5, find the values of p and q.

2.A peacock sitting on the top of a tree of height 10 m observes a snake moving on the ground. If the snake is $10\sqrt{3}$ m away from the base of the tree, then angle of depression of the snake from the eye of the peacock is

3.Two identical cones are joined as shown in the figure. If radius of base is 4 cm and slant height of the cone is 6 cm, then height of the solid is

4.Find the mean and mode of the following data:Class15--2020--2525--3030--3535--4040--45Frequency1210151175

5.OAB is sector of a circle with centre O and radius 7 cm. If length of arc \( \widehat{AB} = \frac{22}{3} \) cm, then \( \angle AOB \) is equal to

6.The number of red balls in a bag is three more than the number of black balls. If the probability of drawing a red ball at random from the given bag is $\dfrac{12}{23}$, find the total number of balls in the given bag.

Similar Mathematics Concepts

Comments

SUBSCRIBE TO OUR NEWS LETTER

1.
The following data shows the number of family members living in different bungalows of a locality:

Number of Members 0−2 2−4 4−6 6−8 8−10 Total
Number of Bungalows 10 p 60 q 5 120

If the median number of members is found to be 5, find the values of p and q.

2.
A peacock sitting on the top of a tree of height 10 m observes a snake moving on the ground. If the snake is $10\sqrt{3}$ m away from the base of the tree, then angle of depression of the snake from the eye of the peacock is

3.
Two identical cones are joined as shown in the figure. If radius of base is 4 cm and slant height of the cone is 6 cm, then height of the solid is

4.
Find the mean and mode of the following data:
Class 15--20 20--25 25--30 30--35 35--40 40--45
Frequency 12 10 15 11 7 5

5.
OAB is sector of a circle with centre O and radius 7 cm. If length of arc \( \widehat{AB} = \frac{22}{3} \) cm, then \( \angle AOB \) is equal to

6.
The number of red balls in a bag is three more than the number of black balls. If the probability of drawing a red ball at random from the given bag is $\dfrac{12}{23}$, find the total number of balls in the given bag.