Introduction to Trigonometry Class 10th Notes - Free NCERT Class 10 Maths Chapter 8 Notes

Introduction to Trigonometry Class 10th Notes - Free NCERT Class 10 Maths Chapter 8 Notes - Download PDF

Edited By Safeer PP | Updated on Jul 29, 2022 04:25 PM IST

NCERT Class 10 Maths Chapter 8 Notes based on the introduction to trigonometry, in which trigonometric identities and ratios were used to find the angles and their measurement. The chapter Introduction to Trigonometry Class 10 notes also includes trigonometry ratios to be learned by students. CBSE Class 10 Maths chapter 8 notes contain systematic explanations of topics using examples and exercises. Class 10 Maths chapter 8 notes include FAQ or frequently asked questions about the chapter. All these topics can be easily downloaded from Class 10 Maths chapter 8 notes pdf download.

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This Story also Contains

Introduction to Trigonometry Class 10 Notes- Topic 1:
Trigonometric Ratios:
Trigonometric Formulas:
Trigonometric Ratios of Some Angles:
Trigonometric Ratios of Complementary Angles:
Significance of NCERT Class 10 Maths Chapter 8 Notes
Class 10 Chapter Wise Notes
NCERT Solutions of Cass 10 Subject Wise
NCERT Class 10 Exemplar Solutions for Other Subjects:

Also, students can refer,

NCERT Class 10 Chapter 1 Notes

Introduction to Trigonometry Class 10 Notes- Topic 1:

Trigonometry can be defined as the science of relationships between sides and right-angle triangles.

Trigonometry Ratios: Trigonometry ratios can be defined as ratios of sides of triangles and are right-angle triangles. Let’s take an example to understand the concepts of trigonometry more clearly. Taking a right-angled triangle, In this, the ratios can be defined according to an acute angle. If one trigonometric ratio of an acute angle is known then we can easily define the other ratios.

Trigonometric Ratios:

The trigonometric ratios can be calculated with the help of a right-angled triangle.

1644383926540

Sin A=opposite side/hypotenuse=BC/AB

Cos A=adjacent side/hypotenuse=AC/AB

Tan A=opposite sidea/djacent side=BC/AC

CosecA=hypotenuse/opposite side=AB/BC

SecA=hypotenuse/adjacent side=AB/AC

CotA=adjacent side/opposite side=AC/BC

Trigonometric Formulas:

tan A=sinA/cosA

cot A=CosA/sinA=1/tanA

SecA=1/cosA

cosecA=1/sinA

sin²A+cos²A=1

sec²A-tan²A=1

cosec²A-cot²A=1

Trigonometric Ratios of Some Angles:

$\angle A$
Sin A	0	$\frac{1}{2}$	$\frac{1}{\sqrt{2}}$	$\frac{\sqrt{3}}{2}$	1
Cos A	1	$\frac{\sqrt{3}}{2}$		$\frac{1}{2}$	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

Trigonometric Ratios of Complementary Angles:

Complementary angles are those angles whose sum is taken out as 90 degrees.

In the case of a right angles triangle, it can be noted that one angle is 90 degrees and in that case, the sum of the other two will be 90 degrees.

Trigonometric ratios for complementary angle will be:

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 with respect to Pythagoras theorem:

1644383926350

According to Pythagoras theorem, in the right-angled triangle at C so for triangle ABC,

(perpendicular)²+(base)²=(hypotenuse)²

(sin²R)+(cos²R)=1

1+(tan²R)=sec²R

1+(cot²R)=cosec²R

Significance of NCERT Class 10 Maths Chapter 8 Notes

Introduction to Trigonometry NCERT notes for Class 10 Maths chapter 8 will help to understand the formulas, statements, rules in detail. Class 10 Maths chapter 8 notes also contain previous year’s questions and NCERT TextBook pdf. Class 10 Introduction to Trigonometry contains identities, ratios, formulas, and a fixed angle table for trigonometric quantities and properties of trigonometry.

Examples-

Calculate the maximum value of 1/secθ where 0°≤θ≤90°.

The maximum value is at 0° when we put this value get,

=1/secθ=1/1=1

Calculate the value when sin=cos, now as per this find value 2tan+cos2.

Given that: sinθ=cosθ

These values are equal to each other at an angle of 45 degrees.

Now, 2tanθ+cos²θ=2tan45°+cos²45°

=2(1)+ (1√2)²

= 2+1/2=5/2

Evaluate the following (1-2cot²45°)/(1+sin²90°)

(1-cot²45°)/(1+sin²90°) =(1-1)/(1+sin²90°)=0

Calculate sin²19°+sin²71° as per formulas given in notes for Class 10 Maths chapter 8

sin²19°+sin²71°=sin²19°+sin²(90°-19°)

=sin²19°+cos²19°=1

When an increase in value of cos from 0 to 90 degrees what type of change can be observed?

cos0°=1 , cos90°=0. When the value of the angle increases from 0 to 90 the value will decrease.

Class 10 Chapter Wise Notes

NCERT Class 10 Maths Chapter 1 Notes

NCERT Class 10 Maths Chapter 2 Notes

NCERT Class 10 Maths Chapter 3 Notes

NCERT Class 10 Maths Chapter 4 Notes

NCERT Class 10 Maths Chapter 5 Notes

NCERT Class 10 Maths Chapter 6 Notes

NCERT Class 10 Maths Chapter 7 Notes

NCERT Class 10 Maths Chapter 8 Notes

NCERT Class 10 Maths Chapter 9 Notes

NCERT Class 10 Maths Chapter 10 Notes

NCERT Class 10 Maths Chapter 11 Notes

NCERT Class 10 Maths Chapter 12 Notes

NCERT Class 10 Maths Chapter 13 Notes

NCERT Class 10 Maths Chapter 14 Notes

NCERT Class 10 Maths Chapter 15 Notes

NCERT Solutions of Cass 10 Subject Wise

NCERT Class 10 Exemplar Solutions for Other Subjects:

NCERT Books for Class 10

NCERT Syllabus for Class 10

Frequently Asked Question (FAQs)

1. Is trigonometry an important chapter for CBSE board exam?

Yes, the NCERT Book Class 10 Chapter Introduction To Trigonometry is an important chapter of NCERT Class 10 Maths Syllabus. 8 to 10 marks questions can be expected from Trigonometry Class 10 Chapter for CBSE board exam

2. What is the value of sin 25.cosec25?

cosec 25=1/sin25 therefore the value of sin 25.cosec25=1

3. Given the value of sin in first quadrant as 0. What is the value of cos in the same quadrant?

sin =0 for 0 degrees. And cos0=1.

4. What is sinA.SecA

sinA.secA=sinA/cosA=tanA

5. Find the value of sin30.cos60

sin30=0.5

cos60=0.5

sin30.cos60=0.25

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