Trigonometric Functions Class 11th Notes - Free NCERT Class 11 Maths Chapter 3 notes

Trigonometric Functions Class 11th Notes - Free NCERT Class 11 Maths Chapter 3 notes - Download PDF

Edited By Ramraj Saini | Updated on Mar 22, 2022 05:09 PM IST

Class 11 Math chapter 3 notes are regarding Trigonometric functions. In chapter 3 we will be going through the concepts of the trigonometric functions in Trigonometric Functions Class 11 notes. This Class 11 Maths chapter 3 notes contains the following topics: Angle, radian, finding angle and radian from formulae, trigonometric functions, domain and range of trigonometric functions, standard formulas, the sign of trigonometric functions, graphs, tables, and many more things to be discussed.

JEE Main Scholarship Test Kit (Class 11): Narayana | Physics Wallah | Aakash | Unacademy

Suggested: JEE Main: high scoring chapters | Past 10 year's papers

New: Aakash iACST Scholarship Test. Up to 90% Scholarship. Register Now

This Story also Contains

NCERT Class 11 Math Chapter 3 Notes
Significance of NCERT Class 11 Maths Chapter 3 Notes:
NCERT Class 11 Notes Chapter Wise.

NCERT Class 11 Math chapter 3 notes are about trigonometric functions and their relations. NCERT Class 11 Math chapter 3 explains all the topics that are important for students from an exam point of view. NCERT Notes for Class 11 Math chapter 3 textbook and notes here below show the same and important points that are essential for exams. FAQ’s that are frequently asked questions will also help students in clarifying their doubts and to think in a very different way.

CBSE Class 11 Maths chapter 3 notes are made similar to that of NCERT where very few changes will be found and the rest of all will be found similar. Notes to fast and easy reference can be downloaded using Class 11 Maths chapter 3 notes pdf download, Class 11 notes Trigonometric functions, class 11 Trigonometric functions notes pdf download.

Also, students can refer,

NCERT Class 11 Math Chapter 3 Notes

Trigonometry: Trigon means three sides and it is a triangle and Metry means measurement.

Angle: Angle is the measure of rotation of ray from its initial point which is generally denoted by θ.

We have both positive and negative angles. They are represented as follows:

1663739751456

Degree:

One degree has 60 minutes and one minute is further divided into 60 seconds. If a ray rotates from one initial point to another end or terminal point then it is said to cover 1/360 th then it is said to be 1° (one degree)

1646894030809

Radian:

It is another unit to measure angles. The angle measured at the centre forming an arc of 1 unit length in a unit circle with a radius being 1 is called a measure of 1 radian.

1646894164076

Formula : = l/r (or ) l= rθ

l= length made by the arc

r= radius of the circle

θ = angle measure.

Relation Between Degree And Radian:

To find the radian measure when degree is given and vice versa.

1 radian = 180°/π

1646894348386

Conventional Measure:

Radian measure = (π/180°) X degree value

Degree measure = (180°/π) X radian value

Trigonometric Functions:

$\\ sin \theta= \frac{opposite \ side}{hypotenuse} \\ cosec \theta = \frac{hypotenuse}{opposite \ side} = \frac{1}{sin \theta} \\ cos \theta= \frac{adjacent\ side}{hypotenuse} \\ sec \theta= \frac{hypotenuse} {adjacent \ side} = \frac{1}{cos \theta } \\ tan \theta = \frac{opposite\ side}{adjacent \ side} = \frac{sin \theta }{cos \theta} \\ cot \theta = \frac{adjacent \ side}{opposite \ side} = \frac{cos \theta}{sin \theta }= \frac{1}{tan \theta} \\ \text{By hypotenuse theorem:} \\ (opposite \ side)^2+(adjacent \ side)^2=(hypotenuse)^2 \\ \text{From the above right angle theorem: } \\ (a)^2+(b)^2=(h)^2$

We have a few identities:

$\\ sin^2 \theta+cos^2 \theta=1 \\ 1 + tan^2 \theta =sec^2 \theta \\ 1+ cot^2 \theta =cosec^2 \theta$

Table to be remembered:

1646896012194

Sign Of Trigonometric Functions:

From the above diagram, we can find the sign of the trigonometric functions.

Some points to remember:

sin(-x) = -sin(x)

cos(-x) = cos(x)

tan(-x) = -tan(x)

cot(-x) = -cot(x)

sec(-x)= sec(x)

cosec(-x) = -cosec(x)

Domain And Range Of Trigonometric Functions:

Function	Domain	Range
sin	R	[-1, 1]
cos	R	[-1, 1]
tan	R – {(2n + 1)(π/2) : n ∈ Z	R
cot	R – {nπ: n ∈ Z}	R
cosec	R – {(nπ : n ∈ Z}	R – (-1, 1)
sec	R – {(2n + 1) (π/2) : n ∈ Z	R – (-1, 1)

1646902370918

Formula:

$\\ sin (x+y)=sinx.cosy+cosx.siny \\ sin (x-y)=sinx.cosy - cosx.siny \\ cos (x+y) = cosx.cosy - sinx.siny \\ cos (x-y) = cosx.cosy + sinx.siny \\ \\$

$\\ tan (x+y) =\frac{ tan x +tan y}{1-tan x.tan y} \\ \\ tan (x-y) = \frac{tan x - tan y}{1+tan x.tan y} \\ \\ cot (x+y) = \frac{cot x.coty-1}{cot x + cot y} \\ \\ cot(x-y) = \frac{cot x.coty+1}{cot y - cot x} \\$

Graphs Of Trigonometric Functions:

1646903138228

Transformation Formulas:

$\\ sin (x+y) + sin (x-y) = 2 sinx.cosy \\ sin (x+y) - sin (x-y) = 2 cosx.siny \\ cos(x+y) + cos(x-y) = 2cosx.cosy \\ cos(x-y) - cos(x+y) = 2 sinx.siny \\$

$\\ sin x + sin y = 2 sin( \frac{x+y}{2}) cos(\frac{x-y}{2}) \\ sin x-sin y = 2 cos(\frac{x+y}{2})sin(\frac{x-y}{2}) \\ cos x + cos y = 2 cos(\frac{x+y}{2})cos(\frac{x-y}{2}) \\ cos x-cos y = -2 sin(\frac{x+y}{2})sin(\frac{x-y}{2}) \\ sin2x=2sinxcosx \\ cos 2x = cos^2 x- sin^2 x =1-2 sin^2 x =2 cos^2 x- 1$

$\\ sin 3x = 3 sinx - 4 sin^3x \\ \\ cos 3x = 4 cos^3 x - 3 cos x \\ \\ tan 3x = \frac{(3 tan x - tan^3x)}{1- 3 tan^2x} \\ \\ cot3x = \frac{3 cot x - cot^3x}{1 - 3cot^2x} \\$

With this topic we conclude NCERT class 11 chapter 3 notes.

The link for the NCERT textbook pdf is given below:

URL: ncert.nic.in/textbook/pdf/kemh103.pdf

Significance of NCERT Class 11 Maths Chapter 3 Notes:

NCERT Class 11 Maths chapter 3 notes will be very much helpful for students to score maximum marks in their 11 board exams. In Trigonometric Functions Class 11 chapter 3 notes we have discussed many topics: Angle, radian, finding angle and radian from formulae, trigonometric functions, domain and range of trigonometric functions, standard formulas, the sign of trigonometric functions, graphs, tables, formulas to remember. NCERT Class 11 Maths chapter 3 is also very useful to cover major topics of the Class 11 CBSE Maths Syllabus.

The CBSE Class 11 Maths chapter 3 is about knowing and learning trigonometric functions. FAQ’s most frequently asked questions that are based on trigonometry that most notes and textbooks do not provide are given and discussed below in the last section. Notes provide an exact idea about the chapter each and every subtopic Class11 chapter 3 Trigonometric Functions pdf download.

NCERT Class 11 Notes Chapter Wise.

NCERT Class 11 Maths Chapter 1 Notes

NCERT Class 11 Maths Chapter 2 Notes

NCERT Class 11 Maths Chapter 3 Notes

NCERT Class 11 Maths Chapter 4 Notes

NCERT Class 11 Maths Chapter 5 Notes

NCERT Class 11 Maths Chapter 6 Notes

NCERT Class 11 Maths Chapter 7 Notes

NCERT Class 11 Maths Chapter 8 Notes

NCERT Class 11 Maths Chapter 9 Notes

NCERT Class 11 Maths Chapter 10 Notes

NCERT Class 11 Maths Chapter 11 Notes

NCERT Class 11 Maths Chapter 12 Notes

NCERT Class 11 Maths Chapter 13 Notes

NCERT Class 11 Maths Chapter 14 Notes

NCERT Class 11 Maths Chapter 15 Notes

NCERT Class 11 Maths Chapter 16 Notes

Subject Wise NCERT Exemplar Solutions

JEE Main Highest Scoring Chapters & Topics

Just Study 40% Syllabus and Score upto 100%

Download EBook

Subject Wise NCERT Solutions

NCERT Books and Syllabus

NCERT Book for Class 11

NCERT Syllabus for Class 11

Frequently Asked Question (FAQs)

1. Do we need to prove the formulas in board exams Trigonometric Functions Class 11 notes?

No, the formulas need not be proved. But they should be remembered for solving the questions.

2. What is the use of Class 11 notes Trigonometric functions in real life?

They are used to find the directions like north, south, east, west.

It is also used to find the distance from a particular point.

3. Can you give some shortcuts to remember the formulas in NCERT notes for Class 11 Math chapter 3?

To remember the sign of the functions in the quadrants we have a trick:

“ ALL SILVER TEA CUPS”.

All - all functions are positive in quadrant 1

Silver- sin, and cosec are positive in quadrant 2

Tea - tan, and cot are positive in quadrant 3

Cups- cos and sec are positive in quadrant 4

4. What is the use of Trigonometry in the medical field according to ncert notes for Class 11 Maths chapter 3?

Trigonometry is used to detect the angle and point of the problem location and for X- rays and many more.

5. Who invented Trigonometry?

“Hipparchus” constructed Trigonometric value tables for the first time.

This can also be obtained from Trigonometric Functions Class 11 notes pdf download.

Also Read

NCERT Class 11 Chemistry Chapter 4 Notes Chemical Bonding and Molecular Structure - Download PDF

NCERT Class 11 Chemistry Chapter 3 Notes - Download PDF

NCERT Class 11 Biology Chapter 19 Notes Excretory Products And Their Elimination- Download PDF Notes

NCERT Class 11 Biology Chapter 22 Notes Chemical Coordination And Integration- Download PDF Notes

Some basic concepts of Chemistry Class 11th Notes - Free NCERT Class 11 Chemistry Chapter 1 Notes - Download PDF

NCERT Class 11 Biology Chapter 21 Notes Neural Control And Coordination- Download PDF Notes

NCERT Class 11 Physics Chapter 5 Notes Laws of Motion - Download PDF

NCERT Class 11 Physics Chapter 3 Notes Motion in a straight Line - Download PDF

NCERT Solutions for Exercise 10.1 Class 11 Maths Chapter 10 - Straight Lines

NCERT Solutions for Miscellaneous Exercise Chapter 16 Class 11 - Probability

NCERT Solutions for Miscellaneous Exercise Chapter 13 Class 11 - Limits and Derivatives

NCERT Solutions for Miscellaneous Exercise Chapter 11 Class 11 - Conic Section

NCERT Exemplar Class 11 Maths Solutions Chapter 12 Introduction to Three Dimensional Geometry

NCERT Exemplar Class 11 Maths Solutions Chapter 10 Straight Lines

NCERT Exemplar Class 11 Maths Solutions Chapter 6 Linear Inequalities

NCERT Exemplar Class 11 Maths Solutions Chapter 16 Probability

NCERT Exemplar Class 11 Maths Solutions Chapter 14 Mathematical Reasoning

NCERT Exemplar Class 11 Maths Solutions Chapter 7 Permutations and Combinations

Articles

High Salary Courses After Class 12 Science

Jul 26, 2024

Ophthalmology Courses After 12th - Eligibility, Duration, Institutes

Jul 26, 2024

BiPC Courses After 12th - Fees, Duration & Top Institutes

Jul 25, 2024

ICSO Sample Papers 2024-25 with Answers For Classes 1 to 10

Jul 25, 2024

NMMS Chhattisgarh Result 2024-25: Check Merit List, Cut Off Marks

Jul 25, 2024

UPTAC Counselling 2024 (Started): Document Verification, Date, Registration, Seat Allotment, Rules, Guidelines

Jul 25, 2024

Essay on Diwali for Students: Short Paragraph, 10 Lines on Deepavali

Jul 24, 2024

How to Study at Home? - Check 10 Tips to Study at Home

Jul 23, 2024

IIM Courses After 12th - Eligibility, Exams, Top Colleges

Jul 19, 2024

Upcoming School Exams

National Means Cum-Merit Scholarship

Application Date:15 July,2024 - 14 August,2024

Eligibility Criteria

Application Process

Exam Pattern

National Institute of Open Schooling 12th Examination

Late Fee Application Date:22 July,2024 - 31 July,2024

Application Process

Exam Pattern

Admit Card

National Institute of Open Schooling 10th examination

Late Fee Application Date:22 July,2024 - 31 July,2024

Application Process

Exam Pattern

Mock Test

Chhattisgarh Board of Secondary Education 12th Examination

Exam Date:23 July,2024 - 12 August,2024

Exam Pattern

Admit Card

Result

Chhattisgarh Board of Secondary Education 10th Examination

Exam Date:24 July,2024 - 08 August,2024

Exam Pattern

Admit Card

Result

View All School Exams

Get answers from students and experts

Popular Questions

A block of mass 0.50 kg is moving with a speed of 2.00 ms^-1 on a smooth surface. It strikes another mass of 1.00 kg and then they move together as a single body. The energy loss during the collision is

Option 1) $0.34\; J$	Option 2) $0.16\; J$
Option 3) $1.00\; J$	Option 4) $0.67\; J$

A person trying to lose weight by burning fat lifts a mass of 10 kg upto a height of 1 m 1000 times. Assume that the potential energy lost each time he lowers the mass is dissipated. How much fat will he use up considering the work done only when the weight is lifted up ? Fat supplies 3.8×10⁷J of energy per kg which is converted to mechanical energy with a 20% efficiency rate. Take g = 9.8 ms⁻² :

Option 1)

2.45×10⁻³ kg

Option 2)

6.45×10⁻³ kg

Option 3)

9.89×10⁻³ kg

Option 4)

12.89×10⁻³ kg

An athlete in the olympic games covers a distance of 100 m in 10 s. His kinetic energy can be estimated to be in the range

Option 1) $2,000 \; J - 5,000\; J$	Option 2) $200 \, \, J - 500 \, \, J$
Option 3) $2\times 10^{5}J-3\times 10^{5}J$	Option 4) $20,000 \, \, J - 50,000 \, \, J$

A particle is projected at 60⁰ to the horizontal with a kinetic energy $K$ . The kinetic energy at the highest point

Option 1) $K/2\,$	Option 2) $\; K\;$
Option 3) $zero\;$	Option 4) $K/4$

In the reaction,

$2Al_{(s)}+6HCL_{(aq)}\rightarrow 2Al^{3+}\, _{(aq)}+6Cl^{-}\, _{(aq)}+3H_{2(g)}$

Option 1) $11.2\, L\, H_{2(g)}$ at STP is produced for every mole $HCL_{(aq)}$ consumed	Option 2) $6L\, HCl_{(aq)}$ is consumed for ever $3L\, H_{2(g)}$ produced
Option 3) $33.6 L\, H_{2(g)}$ is produced regardless of temperature and pressure for every mole Al that reacts	Option 4) $67.2\, L\, H_{2(g)}$ at STP is produced for every mole Al that reacts .

How many moles of magnesium phosphate, $Mg_{3}(PO_{4})_{2}$ will contain 0.25 mole of oxygen atoms?

Option 1) 0.02	Option 2) 3.125 × 10^-2
Option 3) 1.25 × 10^-2	Option 4) 2.5 × 10^-2

If we consider that 1/6, in place of 1/12, mass of carbon atom is taken to be the relative atomic mass unit, the mass of one mole of a substance will

Option 1) decrease twice	Option 2) increase two fold
Option 3) remain unchanged	Option 4) be a function of the molecular mass of the substance.

With increase of temperature, which of these changes?

Option 1) Molality	Option 2) Weight fraction of solute
Option 3) Fraction of solute present in water	Option 4) Mole fraction.

Number of atoms in 558.5 gram Fe (at. wt.of Fe = 55.85 g mol^-1) is

Option 1) twice that in 60 g carbon	Option 2) 6.023 × 10²²
Option 3) half that in 8 g He	Option 4) 558.5 × 6.023 × 10²³

A pulley of radius 2 m is rotated about its axis by a force F = (20t - 5t²) newton (where t is measured in seconds) applied tangentially. If the moment of inertia of the pulley about its axis of rotation is 10 kg m² , the number of rotations made by the pulley before its direction of motion if reversed, is