Chapter 3 Trigonometric Functions

This page contains the complete NCERT notes for Class 11 Math. Chapter 3 - Trigonometric functions. CBSE students looking for Chapter 3 math notes for Year 11 can refer to the NCERT Q&A provided in this article. Vidyakul's top math teachers have created notes for Chapter 3 - Trigonometry Practice. Students can fully trust these NCERT book answers for class exercises and assignments. The notes also helps students quickly review a chapter before exams.

NCERT questions are important for both entrance and competitive exams. Exams like JEE Mains and NEET ask questions from NCERT textbooks. Therefore, solving these NCERT questions helps students build a solid foundation in trigonometric functions.

MATHEMATICS NOTES CHAPTER- 3

Points to Remember

• Trigonometric functions are elementary functions, the argument of which is an angle. Trigonometric functions describe the relation between the sides and angles of a right triangle. Applications of trigonometric functions are extremely diverse. For example, any periodic processes can be represented as a sum of trigonometric functions (Fourier series). These functions often appear in the solution of differential equations and functional equations.

• The trigonometric functions include the following functions: sine, cosine, tangent, cotangent, secant, and cosecant. For each of these functions, there is an inverse trigonometric function.

Formulas

Let us discuss the formulas given in the table below for functions of trigonometric ratios(sine, cosine, tangent, cotangent, secant and cosecant) for a right-angled triangle.

Formulas for Angle θ	Reciprocal Identities
sin θ = Opposite Side/Hypotenuse	sin θ = 1/cosec θ
cos θ = Adjacent Side/Hypotenuse	cos θ = 1/sec θ
tan θ = Opposite Side/Adjacent	tan θ = 1/cot θ
cot θ = Adjacent Side/Opposite	cot θ = 1/tan θ
sec θ = Hypotenuse/Adjacent Side	sec θ = 1/cos θ
cosec θ = Hypotenuse/Opposite	cosec θ = 1/sin θ

Identities

Below are the identities related to trig functions.

Even and Odd functions

The cos and sec functions are even functions; the rest other functions are odd functions.

sin(-x) = -sin x

cos(-x) = cos x

tan(-x) = – tan x

cot(-x) = -cot x

csc(-x) = -csc x

sec(-x) = sec x

Periodic Functions

The trig functions are the periodic functions. The smallest periodic cycle is 2π but for tangent and the cotangent it is π.  

sin(x+2nπ) = sin x

cos(x+2nπ) = cos x

tan(x+nπ) = tan x

cot(x+nπ) = cot x

csc(x+2nπ) = csc x

sec(x+2nπ) = sec x

Where n is any integer.

Pythagorean Identities

When the Pythagoras theorem is expressed in the form of trigonometry functions, it is said to be Pythagorean identity. There are majorly three identities:

• sin2 x + cos2 x = 1    [Very Important]

• 1+tan2 x = sec2 x

• cosec2 x = 1 + cot2 x

These three identities are of great importance in Mathematics, as most of the trigonometry questions are prepared in exams based on them. Therefore, students should memorise these identities to solve such problems easily.

Sum and Difference Identities

• sin(x+y) = sin(x).cos(y)+cos(x).sin(y)

• sin(x–y) = sin(x).cos(y)–cos(x).sin(y)

• cos(x+y) = cosx.cosy–sinx.siny

• cos(x–y) = cosx.cosy+sinx.siny

• tan(x+y) = [tan(x)+tan(y)]/[1-tan(x)tan(y)]

• tan(x-y) = [tan(x)-tan(y)]/[1+tan(x)tan(y)]

Topics and Sub-topics

Before getting into the detailed CBSE NCERT notes for Class 11 Maths Chapter 3, here is a look at the different topics and subtopics in the Trigonometric Functions chapter:

Exercise	Topics
3.1	Introduction
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

 

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