If you are looking for NCERT Maths Solutions For Class 12 Chapter 2, then this article can be very beneficial for you, stay tuned till the end. Along with this, I am going to provide you all the exercises of Inverse Trigonometric Functions like ex 2.2 etc. in PDF form.
By reading this article, you will be able to understand better about inverse trigonometry and I will also give NCERT solutions for class 12 Maths chapter 2 PdF for your better study.
You will get all the exercises in NCERT Solutions for Class 12 Maths Inverse Trigonometric Functions PDF which have been solved in a very simple way which is quite easy to understand.
NCERT Solutions for Class 12 Maths Chapter 2: Inverse Trigonometric Functions is a comprehensive guide for students studying mathematics in Class 12. This chapter introduces students to the basics of inverse trigonometric functions and their properties. Students will learn how to find the inverse of trigonometric functions and solve problems related to them.
here is a table of NCERT Maths Solutions for Class 12 Chapter 2, including Exercise 2.1, Exercise 2.2, and the Miscellaneous Exercise on Inverse Trigonometric Functions:
| Exercise | Name | Number of Problems |
|---|---|---|
| Exercise 2.1 | Relations and Functions | 23 |
| Exercise 2.2 | Inverse Trigonometric Functions | 33 |
| Miscellaneous Exercise | Inverse Trigonometric Functions | 10 |
In addition to Exercise 2.2, this table includes the Miscellaneous Exercise on Inverse Trigonometric Functions, which contains 10 problems covering a variety of topics related to inverse trigonometric functions, such as finding the values of inverse trigonometric functions, simplifying expressions involving inverse trigonometric functions, and solving equations involving inverse trigonometric functions. By working through these exercises and referring to the NCERT Maths Solutions, students can improve their understanding of inverse trigonometric functions and their ability to solve problems in this area.
In This Chapter I will Cover this Topics:
- Inverse Trigonometric Functions Introduction
- Basic Concepts
- Formulas
- Inverse Trigonometric Functions Graphs
- Properties of Inverse Trigonometric Functions
- Inverse Trigonometric Functions Table
The chapter covers important topics such as the definition of inverse trigonometric functions, their domains and ranges, their properties, and their graphs. Students will also learn about the various trigonometric identities and how they can be used to simplify problems involving inverse trigonometric functions.
The solutions provided in this chapter are presented in a step-by-step manner, making it easier for students to understand and apply the concepts. The chapter also includes several solved examples to help students practice and reinforce their understanding of the concepts.
You can Aslo Read: NCERT Maths Solutions for Class 12 Chapter 1
Overall, NCERT Maths Solutions for Class 12 Chapter 2: Inverse Trigonometric Functions is an essential resource for students looking to master the fundamentals of inverse trigonometric functions and their applications in real-world scenarios.
NCERT Maths Solutions For Class 12 Inverse Trigonometric Functions Topics
Inverse Trigonometric Functions Introduction: Inverse trigonometric functions are mathematical functions that give the angle values corresponding to a given trigonometric ratio. They are denoted by functions such as sin^-1, cos^-1, and tan^-1. These functions are useful in solving problems in various fields, including physics, engineering, and mathematics. The domain and range of inverse trigonometric functions are limited to ensure that each input has a unique output.
Basic Concepts of Inverse Trigonometric Functions: The basic concept of inverse trigonometric functions is that they are functions that undo the trigonometric functions. In other words, they give us the angle whose sine, cosine, tangent, or other trigonometric ratio is a given number. These functions are denoted by sin^-1, cos^-1, tan^-1, etc. and are defined for a restricted domain and range to ensure that each input has a unique output. The inverse trigonometric functions are useful in solving problems involving angles and trigonometric ratios in various fields such as mathematics, physics, and engineering.
Formulas of Inverse Trigonometric Functions: Here are some important formulas for inverse trigonometric functions. I will give you a pdf below the formula, in which pdf you will get all the important formulas of inverse trigonometry at one place which will help you a lot in the exam.
- sin^-1(x) + cos^-1(x) = π/2 for -1 ≤ x ≤ 1
- tan^-1(x) + cot^-1(x) = π/2 for x > 0
- sin(sin^-1(x)) = x for -1 ≤ x ≤ 1
- cos(cos^-1(x)) = x for -1 ≤ x ≤ 1
- tan(tan^-1(x)) = x for -π/2 < x < π/2
- sin^-1(x) = cos^-1(√(1-x^2))
- cos^-1(x) = sin^-1(√(1-x^2))
- tan^-1(x) = sin^-1(x/√(1+x^2))
These formulas are useful for simplifying expressions involving inverse trigonometric functions and for solving problems in various fields, including mathematics, physics, and engineering.
Inverse Trigonometric Functions Graphs: The graphs of inverse trigonometric functions are different from the graphs of their corresponding trigonometric functions. Here are some important characteristics of the graphs of the three main inverse trigonometric functions:
- The graph of sin^-1(x) (or arcsin(x)) is a function with domain [-1, 1] and range [-π/2, π/2]. The graph is a reflection of the graph of sin(x) across the line y = x. It is increasing on its domain and has a minimum value of -π/2 at x = -1 and a maximum value of π/2 at x = 1.
- The graph of cos^-1(x) (or arccos(x)) is a function with domain [-1, 1] and range [0, π]. The graph is a reflection of the graph of cos(x) across the line y = x. It is decreasing on its domain and has a minimum value of 0 at x = 1 and a maximum value of π at x = -1.
- The graph of tan^-1(x) (or arctan(x)) is a function with domain (-∞, ∞) and range (-π/2, π/2). The graph is a reflection of the graph of tan(x) across the line y = x. It is increasing on its domain and has no minimum or maximum value.
These graphs are useful in understanding the behavior of inverse trigonometric functions and for solving problems in various fields such as mathematics, physics, and engineering.
Properties of Inverse Trigonometric Functions: Here are some important properties of inverse trigonometric functions:
- Domain and Range: The domain of inverse trigonometric functions is restricted to ensure that each input has a unique output. The range of inverse trigonometric functions is also restricted to ensure that the output is within a certain range.
- Inverse Property: Inverse trigonometric functions are defined as the inverse of their corresponding trigonometric functions. For example, sin^-1(sin(x)) = x for -π/2 ≤ x ≤ π/2.
- Symmetry: The graphs of inverse trigonometric functions are symmetric about the line y = x. For example, sin^-1(x) and cos^-1(x) are reflections of each other across the line y = x.
- Identities: There are several important identities involving inverse trigonometric functions, including sin^-1(x) + cos^-1(x) = π/2 and tan^-1(x) + cot^-1(x) = π/2.
- Inverse Derivatives: The derivatives of inverse trigonometric functions can be expressed in terms of other inverse trigonometric functions or standard functions. For example, the derivative of sin^-1(x) is 1/√(1-x^2) and the derivative of tan^-1(x) is 1/(1+x^2).
These properties are useful for simplifying expressions involving inverse trigonometric functions and for solving problems in various fields such as mathematics, physics, and engineering.
Inverse Trigonometric Functions Table: Here is a table of the inverse trigonometric functions:
| Function | Notation | Domain | Range |
|---|---|---|---|
| Inverse Sine | sin^-1(x) or arcsin(x) | [-1, 1] | [-π/2, π/2] |
| Inverse Cosine | cos^-1(x) or arccos(x) | [-1, 1] | [0, π] |
| Inverse Tangent | tan^-1(x) or arctan(x) | (-∞, ∞) | (-π/2, π/2) |
These functions give us the angle whose sine, cosine, or tangent is a given number. The domain and range of each function are restricted to ensure that each input has a unique output. Inverse trigonometric functions are useful in solving problems involving angles and trigonometric ratios in various fields such as mathematics, physics, and engineering.
Get PDF NCERT Maths Solutions for Class 12 Chapter 2 Exercise 2.1
Are you a Class 12 student studying mathematics and struggling with Inverse Trigonometric Functions? Look no further! NCERT Maths Solutions for Class 12 Chapter 2 Exercise 2.1 provides comprehensive solutions to all your problems.
Exercise 2.1 in Chapter 2 covers the basics of inverse trigonometric functions and their properties. The exercise consists of 12 questions, each of which requires students to find the inverse of a trigonometric function and solve related problems. However, some of the questions can be challenging and require a deep understanding of the concepts.
To help you master this topic, NCERT Maths Solutions for Class 12 Chapter 2 Exercise 2.1 offers step-by-step solutions with detailed explanations. The solutions cover all the important formulas, concepts, and properties related to Inverse Trigonometric Functions Class 12 NCERT PDF. The solved examples in the solutions will also help you practice and reinforce your understanding of the concepts.
Getting the PDF NCERT Maths Solutions for Class 12 Chapter 2 Exercise 2.1 is easy. Simply go to the NCERT website and click on the link for the Chapter 2 Exercise 2.1 solutions. You can then download the PDF and save it to your device for future reference.
With these solutions, you will be able to prepare for your exams and assignments with confidence. You can also use these solutions to solve similar problems from other textbooks or practice papers. By mastering the basics of inverse trigonometric functions, you will be better equipped to solve real-world problems in fields such as engineering, physics, and surveying.
Free PDF of NCERT Maths Solutions for Class 12 Chapter 2 Exercise 2.2
I am going to tell you very well about exercise 2.2 class 12 maths solutions, after which there will be no doubt in your mind because I will also give PDF to you so that you can prepare better for the exam. Can
Inverse trigonometric functions are an important topic in mathematics, and are a key concept in NCERT Maths Solutions for Class 12 Chapter 2 Exercise 2.2. In this exercise, students are introduced to the concept of inverse trigonometric functions and learn how to solve problems involving them.
Inverse trigonometric functions are the inverse functions of the trigonometric functions, such as sine, cosine, and tangent. They give us the angle whose sine, cosine, or tangent is a given number. Inverse trigonometric functions are denoted by sin^-1, cos^-1, and tan^-1.
In NCERT Maths Solutions for Class 12 Chapter 2 Exercise 2.2, students are introduced to the concept of inverse trigonometric functions and learn how to use them to solve problems. The exercise includes a variety of problems that cover topics such as finding the value of inverse trigonometric functions, simplifying expressions involving inverse trigonometric functions, and finding the derivatives of inverse trigonometric functions.
To solve these problems, students must first understand the basic concepts of inverse trigonometric functions, such as their domain and range, symmetry, and inverse property. They must also be familiar with the formulas and identities involving inverse trigonometric functions.
NCERT Solutions for Class 12 Chapter 2 Maths Exercise 2.2 provides students with a variety of problems that help them develop their understanding of inverse trigonometric functions. By solving these problems, students can gain a deeper understanding of the concepts and develop their problem-solving skills.
In summary, inverse trigonometric functions are an important topic in mathematics and play a key role in NCERT Maths Solutions for Class 12 Chapter 2 Exercise 2.2. By mastering the concepts and techniques involved in this exercise, students can develop their problem-solving skills and gain a deeper understanding of this important topic.
Free PDF of Maths Solutions for Class 12 Chapter 2 Exercise 2.2 is readily available online for students to access. This PDF includes step-by-step solutions to problems related to inverse trigonometric functions.
The solutions in the PDF are presented in a clear and concise manner, making it easy for students to understand the concepts involved.
By using this PDF, students can practice and master the concepts and techniques involved in inverse trigonometric functions, and develop their problem-solving skills.
Overall, the Free PDF of Maths Solutions for Class 12 Chapter 2 Exercise 2.2 is a valuable resource for students looking to improve their understanding of inverse trigonometric functions.
Free PDF of NCERT Maths Solutions for Class 12 Chapter 2 Miscellaneous Exercise
Many students leave the various question papers, do not practice its questions, due to which many questions remain in their mind. If you also solve miscellaneous questions then you will be able to score better in the exam because most of the questions are asked from here also. I will also give you Class 12 Maths Chapter 2 Miscellaneous Exercise Solutions, with the help of which you can practice it as well. Let us study more deeply about the various questionnaires.
NCERT Maths Solutions for Class 12 Chapter 2 includes a Miscellaneous Exercise on Inverse Trigonometric Functions, which covers a range of topics related to this important concept. With the availability of free PDF downloads of these solutions, students can easily access and use these valuable resources to improve their understanding and problem-solving skills in this area.
The Miscellaneous Exercise on Inverse Trigonometric Functions consists of 10 problems, which cover a variety of concepts including finding the values of inverse trigonometric functions, simplifying expressions involving inverse trigonometric functions, and solving equations involving inverse trigonometric functions. With step-by-step explanations and examples, the NCERT Maths Solutions for Class 12 Chapter 2 Miscellaneous Exercise make it easier for students to understand and solve these complex problems.
The free PDF downloads of these solutions are available on various educational websites as well as on the official NCERT website. These solutions are useful for students who are studying for their board exams or for those who want to deepen their understanding of inverse trigonometric functions. The PDF format allows students to easily access and use these solutions on their devices, making it more convenient for them to study and practice solving problems anytime, anywhere.
By using the NCERT Maths Solutions for Class 12 Chapter 2 Miscellaneous Exercise, students can improve their problem-solving skills and gain a better understanding of inverse trigonometric functions. These resources are an excellent tool for students who want to succeed in their mathematics studies and beyond.
Conclusion: Inverse Trigonometric Functions is an essential topic in mathematics, particularly in calculus and trigonometry. Inverse trigonometric functions are used to find the angle of a right triangle given the ratio of the sides. The six trigonometric functions, sine, cosine, tangent, cosecant, secant, and cotangent, have inverse functions, which are referred to as the inverse trigonometric functions.
In the Class 12 Inverse Trigonometric Functions chapter, students learn about the definitions, properties, and graphical representations of the inverse trigonometric functions. The chapter covers topics like the domain and range of inverse trigonometric functions, the principal value branches of inverse trigonometric functions, and the graphs of inverse trigonometric functions.
Students are also taught how to solve problems involving inverse trigonometric functions and their applications in real-life situations. The chapter is a crucial foundation for further studies in mathematics and other related fields.
the Class 12 Inverse Trigonometric Functions chapter is an important topic in mathematics that equips students with the knowledge and skills needed to solve problems involving inverse trigonometric functions and their applications.
Today we have studied NCERT Maths Solutions For Class 12 Chapter 2 Inverse Trigonometric Functions thoroughly and also have to know the formulas related to it. Apart from this, we have also provided a PDF of all the exercises of Chapter 2 of Class 12 Maths, with the help of which you can make your preparation better.
FAQs Related to NCERT Maths Solutions for Class 12 Chapter 2 Inverse Trigonometric Functions
What are the NCERT Maths Solutions for Class 12 Chapter 2 Inverse Trigonometric Functions?
NCERT Maths Solutions for Class 12 Chapter 2 Inverse Trigonometric Functions is a set of solutions provided by the National Council of Educational Research and Training (NCERT) for the problems given in the Inverse Trigonometric Functions chapter of the Class 12 maths textbook.
Why are Inverse Trigonometric Functions an important topic in Class 12 maths?
Inverse Trigonometric Functions are an important topic in Class 12 maths because it is a fundamental concept that is used in various fields of mathematics, science, and engineering. The knowledge of inverse trigonometric functions is also essential for solving problems related to triangles and their applications in real-life situations.
Where can I find NCERT Maths Solutions for Class 12 Chapter 2 Inverse Trigonometric Functions?
NCERT Math Solutions for Class 12 Chapter 2 will get inverse trigonometric functions you’ll find on our blog. You will also find a direct pdf on this blog, which allows you to read offline without any problems
How can I use NCERT Maths Solutions for Class 12 Chapter 2 Inverse Trigonometric Functions?
NCERT Maths Solutions for Class 12 Chapter 2 Inverse Trigonometric Functions can be used to solve the problems given in the textbook and practice the concepts learned in the chapter. These solutions can also help students to clarify their doubts and understand the concepts in a better way.
What are some of the important topics covered in NCERT Maths Solutions for Class 12 Chapter 2 Inverse Trigonometric Functions?
Some of the important topics covered in NCERT Maths Solutions for Class 12 Chapter 2 Inverse Trigonometric Functions include the definition of inverse trigonometric functions, their properties, and graphs, the principal value branches of inverse trigonometric functions, and the application of inverse trigonometric functions in real-life situations.
How many exercises are there in class 12 Maths Chapter 2?
There are a total of three exercises in Class 12 Maths Chapter 2 – Inverse Trigonometric Functions. These exercises are designed to cover various topics related to inverse trigonometric functions, such as their properties, graphs, and real-life applications. Each exercise contains a different set of questions and problems that are designed to test the student’s understanding of the concepts taught in the chapter.
Is Maths class 12 tough?
Class 12 Maths can be challenging for some students, as it involves complex concepts and problem-solving techniques. However, with consistent practice and effort, it is definitely possible to understand and excel in Class 12 Maths. It’s important to approach the subject with a positive attitude and a willingness to learn.
One of the key factors that can help students succeed in Class 12 Maths is regular practice. Students should solve a variety of problems, both from the textbook and from other sources, to strengthen their understanding of the concepts and improve their problem-solving skills. They can also seek help from teachers or tutors if they have any doubts or difficulty in understanding the topics.
In addition to this, having a clear understanding of the basics, such as algebra and geometry, can also make it easier to understand the more advanced concepts in Class 12 Maths. Overall, while Class 12 Maths can be challenging, it can also be an interesting and rewarding subject for those who are willing to put in the effort.
Which is the most difficult chapter in class 12 Maths Ncert?
The level of difficulty of chapters in Class 12 Maths NCERT varies from student to student, and what one student may find easy, another may find difficult. However, based on general feedback from students, some of the chapters that are commonly considered to be more challenging include:
Chapter 6: Application of Derivatives
Chapter 7: Integrals
Chapter 8: Application of Integrals
Chapter 9: Differential Equations
Chapter 11: Three-Dimensional Geometry
However, it’s important to note that with consistent practice and effort, any chapter in Class 12 Maths NCERT can be understood and mastered.
What are the 2 inverse trigonometric functions?
There are six trigonometric functions: sine, cosine, tangent, cosecant, secant, and cotangent. Each of these functions has an inverse function, which is called an inverse trigonometric function. The two inverse trigonometric functions that are most commonly used are:
Inverse sine function (arcsin or sin^-1): The inverse sine function takes a value between -1 and 1 as input and returns an angle in the range of -π/2 to π/2 radians or -90° to 90°. It is denoted by arcsin or sin^-1.
Inverse cosine function (arccos or cos^-1): The inverse cosine function takes a value between -1 and 1 as input and returns an angle in the range of 0 to π radians or 0° to 180°. It is denoted by arccos or cos^-1.
