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

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.

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:



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)



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.


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


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:


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:






[-1, 1]



[-1, 1]


R – {(2n + 1)(π/2) : n ∈ Z



R – {nπ: n ∈ Z}



R – {(nπ : n ∈ Z}

R – (-1, 1)


R – {(2n + 1) (π/2) : n ∈ Z

R – (-1, 1)



\\ 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:


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:


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.

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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 - 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.


Get answers from students and experts

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 3.8×107 J 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)


Option 2)

\; K\;

Option 3)


Option 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)


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)


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

Option 1)

less than 3

Option 2)

more than 3 but less than 6

Option 3)

more than 6 but less than 9

Option 4)

more than 9

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