NCERT Solutions for Class 11 Maths Chapter 3 Trigonometric Functions

 

NCERT Solutions for Class 11 Maths Chapter 3 Trigonometric Functions: Trigonometry has various real-time applications. It is used to solve height and distance problems. For example, if we want to measure the height of a building such that we are standing at 50m away from building at point P and the angle of elevation made with the ground at P is 45 degree (as shown in the below figure). Then what will be the height of the building?

Let the height of the building be QR and distance from the base of the building to point P is 50 meter

Using the trigonometric function 

tan(45)=\frac{QR}{QP}\\\Rightarrow 1=\frac{QR}{50}\\\Rightarrow QR=50\ m

There are many other examples such as trigonometry is used in electric circuit analysis, predicting the heights of tides in the ocean, analyzing a musical tone and in seismology, etc. The NCERT Solutions for Class 11 Maths Chapter 3 Trigonometric Functions gives an introduction to basic properties and identities of trigonometric functions. We will use the trigonometric identities in other chapters of Mathematics and throughout the NCERT Physics for both class 11 and 12 also. So it is very important to memorize and understand the basic identities and properties of trigonometric functions mentioned in NCERT Class 11 Maths Chapter 3. with the help of NCERT solutions for class 11 you will be able to understand the topics easily.

The main topics of this chapter are listed below:

3.1 Introduction

3.2 Angles

3.3 Trigonometric Functions

3.4 Trigonometric Functions of Sum and Difference of Two Angles

3.5 Trigonometric Equations

The basic identities of NCERT Solutions for Class 11 Maths Chapter 3 Trigonometric Functions are listed below

 \\1) cos^2x+sin^2x=1\\2)\ 1+tan^2x\ \ \ \ =sec^2x\\3)1+cot^2x\ \ \ \ \ \ =cosec^2x\\4)cos (2n\pi + x) \ = cos x \\5)sin (2n\pi + x) \ = sin x \\6) sin (-x) \ \ \ \ \ \ \ = -sinx \\7) cos (-x) \ \ \ \ \ \ \ = cos x

The above identities you may have studied in your high school classes also. Here are a few more identities that you have to understand from the NCERT Solutions for Class 11 Maths Chapter 3

\\8)cos (x + y) = cos x cos y - sin x sin y \\9)cos (x - y) = cos x cos y + sin x sin y\\10)sin (x + y) = sin x cos y + cos x sin y \\11)sin (x - y) = sin x cos y - cos x sin y

The following identities of the  NCERT Solutions for Class 11 Maths Chapter 3 Trigonometric Functions have some conditions

If  angles x, y and (x ± y) is not an odd multiple of π 2, then

\\a) tan(x+y)=\frac{tanx+tany}{1-tanxtany}\\b)tan(x-y)=\frac{tanx-tany}{1+tanxtany}

If  angles x, y and (x ± y) is not a multiple of π, then

\\a) cot(x+y)=\frac{cotxcoty-1}{cotx+coty}\\b)cot(x-y)=\frac{1+cotxcoty}{coty-cotx}

There are a few more identities in the NCERT Class 11 Maths Chapter 3 Trigonometry which can be derived using the above identities. Try to derive it your self.

Here are the NCERT Solutions for Class 11 Maths Chapter 3 Trigonometric Functions.

NCERT Solutions for Class 11 Maths Chapter 3 Trigonometric Functions- Exercise 3.1

NCERT Solutions for Class 11 Maths Chapter 3 Trigonometric Functions- Exercise 3.2

NCERT Solutions for Class 11 Maths Chapter 3 Trigonometric Functions- Exercise 3.3

NCERT Solutions for Class 11 Maths Chapter 3 Trigonometric Functions- Miscellaneous

NCERT Solutions for Class 11 Maths- Chapter-wise

Chapter-1

Sets

Chapter-2

Relations and Functions

Chapter-4

Principal of Mathematical Induction

Chapter-5

Complex Numbers and Quadratic equations

Chapter-6

Linear Inequalities

Chapter-7

Permutation and Combinations

Chapter-8

Binomial Theorem

Chapter-9

Sequences and Series

Chapter-10

Straight Lines

Chapter-11

Conic Section

Chapter-12

Introduction to Three Dimensional Geometry

Chapter-13

Limits and Derivatives

Chapter-14

Mathematical Reasoning

Chapter-15

Statistics

Chapter-16

Probability

NCERT Solutions for Class 11 - Subject Wise

NCERT Solutions for Class 11 Biology

NCERT Solutions for Class 11 Maths

NCERT Solutions for Class 11 Chemistry

NCERT Solutions for Class 11 Physics

 

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