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.

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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:

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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)

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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.

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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

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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:

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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)

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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:

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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

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