NCERT Solutions for Class 11 Maths Chapter 3 Exercise 3.2 PDF
NCERT Solutions for Class 11 Maths Chapter 3 Exercise 3.2 has been provided here. Students can refer to these solutions before their examination for better understanding.
Ananya Gupta22 Jan, 2025
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NCERT Solutions for Class 11 Maths Chapter 3 Exercise 3.2: Exercise 3.2 of Chapter 3 in Class 11 Maths focuses on understanding the signs of trigonometric functions in different quadrants, along with their domain and range.
This exercise helps students analyze the behavior of trigonometric functions such as sine, cosine, tangent, and others based on the angle's position on the coordinate plane. The solutions provide step-by-step explanations, ensuring students grasp these fundamental concepts effectively. By practicing these problems, students can develop a strong foundation for advanced trigonometry topics.NCERT Solutions for Class 11 Maths Chapter 3 Exercise 3.2 Overview
Exercise 3.2 focuses on key aspects of trigonometric functions, including their sign conventions , domain , and range . Students learn how the sign of trigonometric functions - such as sine, cosine, tangent, cosecant, secant, and cotangent - varies depending on the angle's position in the four quadrants. The exercise also emphasizes understanding the domain (the set of input angles for which the functions are defined) and the range (the set of possible output values for each function). It introduces concepts such as periodicity and the behavior of these functions on a coordinate plane. Through detailed examples and exercises, students gain a clear understanding of how to analyze and solve problems involving the properties of trigonometric functions, laying the groundwork for more advanced topics in trigonometry.Class 11 Maths Chapter 3 Exercise 3.2 Questions and Answers PDF
The PDF for NCERT Solutions to Class 11 Maths Chapter 3 Exercise 3.2 provides detailed answers to all questions, focusing on the sign conventions, domain, and range of trigonometric functions. The solutions are presented step-by-step, making it easier for students to understand the concepts and apply them effectively in problem-solving. This resource is designed to enhance conceptual clarity and exam preparation. The PDF link is available below for easy access and download.Class 11 Maths Chapter 3 Exercise 3.2 Questions and Answers PDF
Find the values of the other five trigonometric functions in Exercises 1 to 5.
1. cos x = -1/2, x lies in third quadrant.
Solution:
2. sin x = 3/5, x lies in second quadrant.
Solution:
It is given that sin x = 3/5 We can write it as
We know that
sin
2
x + cos
2
x = 1
We can write it as
cos
2
x = 1 – sin
2
x
3. cot x = 3/4, x lies in third quadrant.
Solution:
It is given that cot x = 3/4 We can write it as
We know that
1 + tan
2
x = sec
2
x
We can write it as
1 + (4/3)
2
= sec
2
x
Substituting the values
1 + 16/9 = sec
2
x
cos
2
x = 25/9
sec x = ± 5/3
Here x lies in the third quadrant, so the value of sec x will be negative
sec x = – 5/3
We can write it as
4. sec x = 13/5, x lies in fourth quadrant.
Solution:
It is given that sec x = 13/5 We can write it as
We know that
sin
2
x + cos
2
x = 1
We can write it as
sin
2
x = 1 – cos
2
x
Substituting the values
sin
2
x = 1 – (5/13)
2
sin
2
x = 1 – 25/169 = 144/169
sin
2
x = ± 12/13
Here x lies in the fourth quadrant, so the value of sin x will be negative
sin x = – 12/13
We can write it as
5. tan x = -5/12, x lies in second quadrant.
Solution:
It is given that tan x = – 5/12 We can write it as
We know that
1 + tan
2
x = sec
2
x
We can write it as
1 + (-5/12)
2
= sec
2
x
Substituting the values
1 + 25/144 = sec
2
x
sec
2
x = 169/144
sec x = ± 13/12
Here x lies in the second quadrant, so the value of sec x will be negative
sec x = – 13/12
We can write it as
Find the values of the trigonometric functions in Exercises 6 to 10.
6. sin 765°
Solution:
We know that values of sin x repeat after an interval of 2π or 360° So we get
By further calculation
= sin 45
o
= 1/
√
2
7. cosec (–1410°)
Solution:
We know that values of cosec x repeat after an interval of 2π or 360° So we get
By further calculation
= cosec 30
o
= 2
8.
Solution:
We know that values of tan x repeat after an interval of π or 180° So we get
By further calculation
We get
= tan 60
o
=
√
3
9.
Solution:
We know that values of sin x repeat after an interval of 2π or 360° So we get
By further calculation
10.
Solution:
We know that values of tan x repeat after an interval of π or 180° So we get
By further calculation
Benefits of Solving NCERT Solutions for Class 11 Maths Chapter 3 Exercise 3.2
- Understanding Sign Conventions : This exercise helps students learn how the signs of trigonometric functions vary across different quadrants, an essential concept for advanced trigonometry.
- Grasping Domain and Range : Students gain a clear understanding of the domain and range of trigonometric functions, which is fundamental for analyzing their behavior.
- Improved Problem-Solving Skills : The step-by-step solutions guide students in applying theoretical knowledge to practical problems, enhancing their analytical and reasoning abilities.
- Exam-Oriented Preparation : These solutions align with the CBSE syllabus and provide practice with questions likely to appear in exams, boosting confidence and readiness.
- Foundation for Advanced Topics : Mastering these concepts prepares students for more complex topics like trigonometric equations, identities, and calculus.
NCERT Solutions for Class 11 Maths Chapter 3 Exercise 3.2 FAQs
Why is understanding sign conventions important?
Sign conventions help determine whether a trigonometric function is positive or negative in a specific quadrant, which is crucial for solving advanced trigonometric problems.
What is the domain and range of a trigonometric function?
The domain includes all input values (angles) for which a trigonometric function is defined, while the range consists of all possible output values (ratios).
How does this exercise help in exam preparation?
The problems in Exercise 3.2 align with the CBSE syllabus, providing practice with questions that are important for exams and competitive tests.
How does solving Exercise 3.2 prepare students for higher studies?
This exercise builds a strong foundation in understanding trigonometric properties, which is essential for advanced topics like calculus and differential equations.
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