CBSE Class 11 Maths Revision Notes Chapter 3

Class 11 Mathematics Revision Notes for Chapter-3 Trigonometric Functions

One of the most crucial topics in Class 11 Mathematics is trigonometry functions. It describes how a right-angle triangle’s sides and angles relate to one another. Students looking to understand the fundamentals of trigonometric functions should refer to the Class 11 Mathematics Chapter 3 Notes. 

The Chapter 3 Mathematics Class 11 Notes give students a quick overview of all the topics and formulas covered, which gives them more confidence when solving questions based on trigonometry.

For convenience, these trigonometric functions Class 11 Mathematics Notes Chapter 3 are organised systematically. It is advised that the students consult these Class 11 Mathematics Notes Chapter 3 as needed to prepare the entire chapter effectively. 

  1. The Meaning of Trigonometry

Tri   Gon   Metron 

 ↓       ↓          ↓

3   sides   measure 

As a result, this branch of mathematics was developed in antiquity to count the three sides, three angles, and six parts of a triangle. There are many applications for time-trigonometric functions today. In a right-angled triangle, the two fundamental functions are the sine and cosine of an angle, and there are four additional derivative functions.

  1. Basic Trigonometric Identities

(a) sin2θ + cos2 θ=1:−1⩽sinθ⩽1;−1⩽cosθ⩽1∀θ∈R

(b) sec2θ − tan2θ=1:|secθ|⩾1∀θ∈R

(c) cosec2θ − cot2 θ=1:|cosecθ|⩾1∀θ∈R

Trigonometric Ratios of Standard Angles:

The following can be given as the relationship between these trigonometric identities and the triangle sides:

  • Sine θ = Opposite/Hypotenuse
  • Cos θ = Adjacent/Hypotenuse
  • Tan θ = Opposite/Adjacent
  • Cot θ = Adjacent/Opposite
  • Cosec θ = Hypotenuse/Opposite
  • Sec θ = Hypotenuse/Adjacent
  1. Trigonometric Ratios of Allied Angles

Using the trigonometric ratio of allied angles, we can calculate the trigonometric ratios of angles of any value.

  1. Sin(–θ)=–Sinθ
  2. Cos(–θ)=Cosθ
  3. Tan(–θ)=–Tanθ
  4. Sin(90o–θ)=Cosθ
  5. Cos(90o–θ)=Sinθ
  6. Tan(90o–θ)=Cotθ
  7. Sin(180o–θ)=Sinθ
  8. Cos(180o–θ)=–Cosθ
  9. Tan(180o–θ)=–Tanθ
  10. Sin(270o–θ)=–Cosθ
  11. Cos(270o–θ)=–Sinθ
  12. Tan(270o–θ)=Cotθ
  13. Sin(90o+θ)=Cosθ
  14. Cos(90o+θ)=–Sinθ
  15. Tan(90o+θ)=–Cotθ
  16. Sin(180o+θ)=–Sinθ
  17. Cos(180o+θ)=–Cosθ
  18. Tan(180o+θ)=Tanθ
  19. Sin(270o+θ)=–Cosθ
  20. Cos(270o+θ)=Sinθ
  21. Tan(270o+θ)=–Cotθ
  1. Trigonometric Functions of Sum or Difference of Two Angles

(a) sin(A+B)=sinA cosB+cosAsinB

(b) sin(A−B)=sinA cosB−cosAsinB

(c) cos(A+B)=cosA cosB−sinAsinB

(d) cos(A−B)=cosA cosB+sinAsinB

(e) tan(A+B)=tanA+tanB÷ 1−tanAtanB

(f) tan(A−B)=tanA−tanB÷1+tanAtanB

(g) cot(A+B)=cotA cotB−1cotB÷cotB+cotA

(h)cot(A−B)=cotA cotB+1÷cotB−cotA

 

  1. Multiple Angles and Half Angles

(a) sin2A=2sinAcosA

(b) sin3A=3sinA−4 sin3A

(c) cos3A=4cos3A−3cosA

  1. Transformation of Products into Sum or Difference of Sines & Cosines

 

  1. a) 2sinAcosB=sin(A+B)+sin(A−B)

(b) 2cosAsinB=sin(A+B)−sin(A−B)

(c) 2cosAcosB=cos(A+B)+cos(A−B)

(d) 2sinAsinB=cos(A−B)−cos(A+B)

  1. Factorisation of the Sum or Difference of Two Sines or Cosines
  2. Important Trigonometric Ratios
  3. Conditional Identities
  4. Sine and Cosine Series
  5. Graphs of Trigonometric Functions
  6. Trigonometric Equations

Equations utilising trigonometric functions with unknown angles are known as trigonometric equations.

A solution is the value of the unknown angle that answers a trigonometric equation.

As a result, the trigonometric equation is categorised as follows and can have any number of solutions:

(i) Principal Solution

The values of sin x and cos x will repeat after an interval of two, as is known. The values of tan x will be repeated in the same way after an interval of ?.

(ii) General solution

Any trigonometric equation solution that involves the integer ‘n’ is referred to as a general solution. In addition, the set of integers is indicated by the character “Z.”

14.1 Results

Steps to Solve Trigonometric Functions:

The steps for solving trigonometric equations are as follows:

Step 1: Use the sine or cos function to decompose the trigonometric equation into a single trigonometric ratio.

Step 2: Factor the ratio into the trigonometric polynomial that is given.

Step 3: After calculating the general answer to each factor, write it down.

Note:

  1. Unless specifically stated otherwise, zero is regarded as an integer in this chapter.
  2. The general answer should be given unless it must fall within a specific interval or range.
  3. The angle’s main value is denoted by α. (An angle with the least numerical value is the main value.)

Download Free Trigonometric Functions Class 11 Notes 

Students in Class 11 can easily access the trigonometric functions Class 11 Mathematics Chapter 3 Notes whenever and wherever they like. Those who refer to the Class 11 Mathematics Chapter 3 Notes can regularly practise the concepts explained which will help them score better grades and make learning an enjoyable experience.

Chapter 3 Mathematics Class 11 Notes provide a concise summary of the all concepts in the chapter to help students remember them and build confidence before attempting the trigonometric exam questions. Chapter 3 Mathematics Class 11 Notes are crucial and helpful because they enable them to thoroughly review the entire chapter prior to the exam.

Class 11 Mathematics Notes Chapter 3 are meticulously prepared by subject matter experts at Extramarks while keeping in mind the updated CBSE syllabus and guidelines.

Extensive formulas and questions in each chapter of the Class 11 Mathematics textbook can be learnt and solved easily with the help of revision notes. As a result, the Trigonometric Functions Chapter 3 Mathematics Class 11 Notes are essential to helping students easily memorise the topics in this chapter. 

A Few Glimpses of Class 11 Chapter 3 Trigonometric Functions

The Greek words “trignon” and “metron,” which denote “measuring the slides of a triangle,” are the roots of the English word trigonometry. This subject was initially established to address a triangle-related geometrical puzzle. Engineers, sea captains, surveyors looking for new lands, and other professionals used trigonometry. Trigonometry is currently used in many fields, including the science of seismology, designing electric currents, and estimating the heights of ocean tides.

Students must have studied the trigonometric ratios of an acute angle as a ratio of the sides of the right-angle triangle in their earlier classes, as well as the use of trigonometric ratios and trigonometric identities. They will study the properties of trigonometry functions and calculate trigonometry ratios in this chapter.

Trigonometric Functions

Trigonometry functions, also referred to as circular functions, describe how the sides and angles of a right-angle triangle relate to one another. It implies that these trigonometric functions are used to derive the relationship between the sides and angles of a right-angle triangle. The main division of trigonometric functions is into sine, cosine, and tangent angles. And from the basic trigonometric functions, the other three functions, such as cotangent, secant, and cosecant, are derived. For each of the aforementioned trigonometric functions, there is an inverse trigonometric function.

Topic and Subtopics Covered in Class 11 Chapter 3 Trigonometric Functions

The different topics and subtopics covered in Class 11 Chapter 3 Trigonometric Functions include:

3.1: Introduction to Chapter

3.2: Angles

3.2.1: Degree Measure

3.2.2: Radian Measure

3.2.3: Relation between radian and real numbers

3.2.4: Relation between degree and radian

3.3: Trigonometric Functions

3.3.1: Sign of Trigonometric Functions

3.3.2: Domain And Range of Trigonometric Functions

3.4: Trigonometric Functions of Sum and Difference of Two Angles

3.5: Trigonometric Equations

Get a quick overview of all the topics and subtopics covered in the chapter by accessing the free Trigonometric Functions Class 11 Mathematics Notes Chapter 3 right away. Students will understand all of the topics mentioned above better with the help of these revision notes because they are well-structured for simple chapter revision. Referring to these Class 11 Mathematics Notes Chapter 3 will boost their confidence and is a great tool for exam preparations. 

Benefits of Extramarks Class 11 Mathematics Notes Chapter 3

The following benefits of Extramarks Class 11 Mathematics Notes Chapter 3 are described.

  • Class 11 Mathematics Notes Chapter 3 offers a precise summary of the chapter.
  • The key theorems and formulas relating to the trigonometric function can be quickly and effectively reviewed by students.
  • By consulting Chapter 3 Mathematics Class 11 Notes, students can save valuable time.
  • Written by subject matter experts, students will be able to quickly recall all the chapter’s important topics.
  • Students can use Class 11 Mathematics Notes Chapter 3 to thoroughly review trigonometry in the days leading up to the test.

FAQs (Frequently Asked Questions)

Sine, cosine, tan, cosec, sec, and cot are the six trigonometric functions.

Chapter 3 of Class 11 Trigonometry Mathematics first provides a brief overview of the chapter before discussing the various trigonometric functions like sin, cos, and tan. This chapter covers topics like angles, radian and degree measurements, their relationships, the sign of trigonometric functions, their sums and differences, related equations, and the relationship between real numbers and radian values. Students must understand all of the topics and subtopics to do well in the exams.