# NCERT Exemplar Class 11 Maths Solutions Chapter 3 Trigonometric Functions

**NCERT Exemplar Class 11 Maths solutions chapter 3 Trigonometric Functions** is considered a very important chapter for practical use, and application in various different fields and also for the exams. NCERT Exemplar Class 11 Maths chapter 3 solutions give a brief procedure and explanation about angles along with degree and radian measure. It also establishes a relationship between radian and real numbers, and radian and degree measure. Class 11 Maths NCERT Exemplar solutions chapter 3 also covers a variety of questions relating to a conversion of degrees to radian and vice versa through established relation between them through the use of notational convention.

Question:23

If has α and β as its roots, then prove that [Hint: Use the identities ]

Answer:

Since are the roots of the equation i)we have tanα and tanβ are the roots of ii)

Question:33

Which of the following is not correct?

A.

B.

C.

D.

Answer:

The answer is the option (c)

is correct since

Question:39

Which of the following is correct?

A.

B.

C.

D.

[Hint: approx.]

Answer:

The answer is the option (b).

If increases then the value of also increases. \\\\

So,

Hence, b is correct.

Question:41

The minimum value of is

A. 5

B. 9

C. 7

D. 3

Answer:

The answer is the option (d).

Hence, (d) is the correct option.

Question:42

The value of is equal to

A.

B.

C.

D. None of these

Answer:

The answer is the option (a).

Hence, a is correct.

Question:44

The value of is

A. –1

B. 0

C. 1

D. Not defined

Answer:

The answer is the option (c).

(c) is correct.

Question:45

is equal to

A.

B.

C.

D.

[Hint: Use ]

Answer:

The answer is the option (b).

Hence, the correct option is (b).

Question:50

If , then the value of is equal to

A. 1

B. 1/2

C. 0

D. –1

Answer:

The answer is the option (c).

Question:51

If then the value of is

A. 1

B. 2

C. –2

D. Not defined

Answer:

Hence, correct option is (b).

Question:52

If and θ lies in third quadrant then the value of is

A.

B.

C.

D.

Answer:

The answer is the option (c)

Hence, correct option is (c).

Question:53

Number of solutions of the equation lying in the interval is

A. 0

B. 1

C. 2

D. 3

Answer:

The answer is the option (c).

Since the equation is a quadratic equation in . So, there will be two solutions.

Hence, correct option is (c).

Question:54

Answer:

The answer is the option (a).

Hence, correct option is (a).

Question:55

If A lies in the second quadrant and , then the value of is equal to

A.

B.

C.

D.

Answer:

The answer is the option (b).

[A lies in second quadrant]

[A lies in second quadrant]

Hence, correct option is (b).

Question:57

If then is equal to

A.

B.

C.

D.

Answer:

The answer is the option (b).

Hence, correct option is (b).

Question:59

Answer:

The answer is the option (d).

Hence, correct option is (d).

Question:61

Fill in the blanks

If then the numerical value of k is

Answer:

Question:67

Answer:

The maximum distance from a point on the graph of equation (i) from x - axis

Question:69

True and False

The equality holds for some real value of A.

Answer:

Given that

Since the maximum value of sin A is 1 but for sin 2A and sin 3A it is not equal to 1. So, it is not possible.

Hence, the statement is ’false’.

Question:70

True and False

is greater than

Answer:

which is not possible because value of sine is in increasing order

Hence, the statement is ‘false’

Question:72

True and False

One value of θ which satisfies the equation lies between 0 and 2π

Answer:

Given equation is

which is not possible

Hence, the given statement is ‘false’

Question:76

Answer:

Thus, (a) - (iv) , (b) - (i), (c) -(ii), (d) - (iii)

**Important Notes of NCERT Exemplar Class 11 Maths Solutions Chapter 3 Trigonometric Functions**

Trigonometry is an ancient concept which in ancient times was used to solve problems relating to triangles and geometry, but it has extended its use to various different fields in the present times including varied areas of studies. It was derived from Greek words meaning, “measuring the sides of a triangle” which has widened its scope to much more than the original meaning. It is basically used to measure length, height and angles of different triangles with its reach in real-life practical situations. NCERT Exemplar solutions for Class 11 Maths chapter 3 extends studying trigonometric ratios to any angle regarding or concerning radian measure and interpreting and representing it as a trigonometric ratio with the help of diagrams for a better understanding.

Students can make use of NCERT Exemplar Class 11 Maths solutions chapter 3 pdf download for further learning.

**Main Subtopics of NCERT Exemplar Class 11 Maths Solutions Chapter 3**

The topics covered in the chapter are as follows:

- 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
- 3.3.1Sign 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

**What will the students learn from NCERT Exemplar Class 11 Maths Solutions Chapter 3?**

The students will learn a variety of concepts from NCERT Exemplar solutions for Class 11 Maths chapter 3 which has a wide range of application in different fields such as engineering, sound engineers, architects, astronauts, surveyors, physicist, and much more for future references. NCERT Exemplar Class 11 Maths solutions chapter 3 is also given importance since it has various applications in real life and could be connected to routine activities that happen around us. It is even used in the gaming industry, IT sector, construction of bridges, buildings, mountains, the inclination of floors, roofs, marine biology, criminal investigations, wide use in physics for derivations and explanations, and much more. The uses of trigonometry in these many fields justify its use for inexhaustible purposes and its importance for students belonging or deciding to enter any field or subject in the future.

**NCERT Solutions for Class 11 Mathematics Chapters**

**Important Topics To Cover From NCERT Exemplar Class 11 Maths Solutions Chapter 3 Trigonometric Functions**

· NCERT Exemplar Class 11 Maths chapter 3 solutions give explanation, and interpretation of different trigonometric functions for sin x, cos x, sec x, cot x, cosec x, and tan x along with values of trigonometric ratios for 0º, 30º, 45º, 60º, 90º, 180º, 270º and 360º along with the sign convention of these trigonometric functions.

· Class 11 Maths NCERT Exemplar solutions chapter 3 also covers the range and domain of trigonometric functions with the help of diagrammatic representation of the same. This chapter also extends to the trigonometric functions of sum and difference of two angles with a variety of questions and illustrations to be done for the same.

· NCERT Exemplar class 11 Maths solutions chapter 3 concludes with insight on trigonometric equations that involve equations containing trigonometric functions of any variable.

**Check Chapter-Wise NCERT Solutions of Book**

Chapter-1 | |

Chapter-2 | |

Chapter-3 | Trigonometric Functions |

Chapter-4 | |

Chapter-5 | |

Chapter-6 | |

Chapter-7 | |

Chapter-8 | |

Chapter-9 | |

Chapter-10 | |

Chapter-11 | |

Chapter-12 | |

Chapter-13 | |

Chapter-14 | |

Chapter-15 | |

Chapter-16 |

**NCERT Exemplar Class 11 Solutions**

**Read more NCERT Solution subject wise -**

- NCERT Solutions for Class 11 Maths
- NCERT Solutions for Class 11 Physics
- NCERT Solutions for Class 11 Chemistry
- NCERT Solutions for Class 11 Biology

**Also, read NCERT Notes subject wise -**

- NCERT Notes for Class 11 Maths
- NCERT Notes for Class 11 Physics
- NCERT Notes for Class 11 Chemistry
- NCERT Notes for Class 11 Biology

**Also Check NCERT Books and NCERT Syllabus here:**

## Frequently Asked Question (FAQs) - NCERT Exemplar Class 11 Maths Solutions Chapter 3 Trigonometric Functions

**Question: **Who can use these solutions of the NCERT chapter?

**Answer: **

Those who are prepping for their board exams and for those who are planning to appear in their JEE Main exam or any other engineering entrance exam.

**Question: **What all topics are covered in this chapter?

**Answer: **

This chapter covers everything related to trigonometric functions, their properties, angles, trigonometric equations, etc.

**Question: **Who has prepared these NCERT exemplar Class 11 maths solutions chapter 3?

**Answer: **

These solutions are prepared by other experienced maths teachers and team so as to include every detail of the solution with no mistake.

**Question: **How to make use of these solutions?

**Answer: **

Students can practice the questions, and while doing so, these Class 11 Maths NCERT exemplar solutions chapter 3 will act as a reference while studying.

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