case study on inverse trigonometric functions class 12

CBSE Case Study Questions for Class 12 Maths Inverse Trigonometric Functions Free PDF

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CBSE Case Study Questions for Class 12 Maths Inverse Trigonometric Functions PDF

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Class 12 Maths: Case Study of Chapter 2 Inverse Trigonometric Functions PDF Download

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In Class 12 Boards there will be Case studies and Passage Based Questions will be asked, So practice these types of questions. Study Rate is always there to help you. Free PDF Download of CBSE Class 12 Mathematics Chapter 2 Inverse Trigonometric Functions Case Study and Passage Based Questions with Answers were Prepared Based on Latest Exam Pattern. Students can solve NCERT Class 12 Maths Inverse Trigonometric Functions  to know their preparation level.

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In CBSE Class 12 Maths Paper, There will be a few questions based on case studies and passage-based as well. In that, a paragraph will be given, and then the MCQ questions based on it will be asked.

Inverse Trigonometric Functions Case Study Questions With answers

Here, we have provided case-based/passage-based questions for Class 12 Mathematics  Chapter 2 Inverse Trigonometric Functions

Case Study/Passage-Based Questions

Case Study 1:

Two men on either side of a temple of 30 meters high observe its top at the angles of elevation α and β respectively. (as shown in the figure above). The distance between the two men is 40√3 metres and the distance between the first person A and the temple is 30√3 meters. ∠CAB = α =

• A.sin -1 (2/√3)
• B.sin -1 (1/2)
• C.sin −1 (2)
• D.sin −1 (√3/2)

Answer: (B)

Hope the information shed above regarding Case Study and Passage Based Questions for Class 12 Maths Chapter 2 Inverse Trigonometric Functions with Answers Pdf free download has been useful to an extent. If you have any other queries of CBSE Class 12 Mathematics Inverse Trigonometric Functions Case Study and Passage Based Questions with Answers, feel free to comment below so that we can revert back to us at the earliest possible. By Team Study Rate

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Case Study Questions for Class 12 Maths Chapter 2 Inverse Trigonometric Functions

• Last modified on: 1 year ago
• Reading Time: 4 Minutes

Case Study Questions:

Question 1:

The Government of India is planning to fix a hoarding board at the face of a building on the road of a busy market for awareness on COVID-19 protocol. Ram, Robert and Rahim are the three engineers who are working on this project. ‘A’ is considered to be a person viewing the hoarding board 20 metres away from the building, standing at the edge of a pathway nearby, Ram Robert and Rahim suggested to the film to place the hoarding board at three different locations namely C, D and E. ‘C’ is at the height of 10 metres from the ground level. For the viewer ‘A’, the angle of elevation of ‘D’ is double the angle of elevation of ‘C’. The angle of elevation of ‘E’ is triple the angle of elevation of ‘C’ for the same viewer.

Look at the figure given and based on the above information answer the following:

(i) Measure of ∠CAB = (a) tan –1 (2) (b) tan –1 (1/2) (c) tan– 1 (1) (d) tan –1 (3)

(ii) Measure of ∠DAB = (a) tan –1 (3/4) (b) tan –1 (3) (c) tan –1 (4/3) (d) tan –1 (4)

(iii) Measure of ∠EAB (a) tan –1 (11) (b) tan –1 (3) (c) tan –1 (2/11) (d) tan –1 (11/2)

(iv) A’ is another viewer standing on the same line of observation across the road. If the width of the road is 5 meters, then the difference between ∠CAB and ∠CA’B is (a) tan –1 (1/12) (b) tan –1 (1/8) (c) tan –1 (2/5) (d) tan –1 (11/21)

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Case study inverse trigonometry 2 chapter 2 class 12

Case study chapter 2 (inverse trigonometry).

Case study 2:- Read the following and answer the question.(Case study inverse trigonometry 1)

  Two men on either side of a temple 30 metres high observes its top at the angles of elevation α and β respectively. (as shown in the figure above). the distance between the two men is 40√3 metres and the distance between the first person A and the temple is 30√3 metres.

(i) ∠CAB = α =

(ii) ∠CAB = α =

(iii) ∠BCA = β = 

(iv) ∠ABC = 

(a) π/4                       (b) π/6

(c) π/2                         (d) π/3

(a) (-1, 1), (0, π)                (b) [-1, 1], (0, π)

(c) [-1, 1], [0, π]                 (d) (-1, 1), [-π/2, π/2]

Solution :We have

(i) Answer (b)

Now in ΔABD (right angled)

(ii) Answer (c) 

We have from (i)

(iii) Answer (d)

In right ΔBCD, we have

(iv) Answer (c)

ΔABC, we have,

∠ABC + ∠BAC  +  ∠ACB = 180°

⇒  ∠ABC + α + β = 180°

⇒  ∠ABC + 30 + 60 = 180

⇒  ∠ABC = 90

⇒  ∠ABC = π/2

(v) Answer (c)

Domain =[-1, 1]

Range = [0, π]

Some other Case study problem

Case study 1:-  The government of India is planning to fix a hoarding board at the face of a building on yhe road of bisy market for awaeeness on COVID-19 protocol. Ram , Robert and Rahim are the three engineers who are working on this project. “A” is considered to be person viewing the hoarding board 20 metres away from the building , standing at the edge of a pathwaynearby . Ram , Robert and Rahim suggested to the firm to place the hoarding board at three different locations namely C, D and E. “C” is at the height of  10 metres from the ground level. for the viewer A, the angle of elevation of “D” is double the angle of elevation of “C” the angle of elevation of “E” is triple the angle of elevation of “C” for the same viewer.(Case study inverse trigonometric 1 )

Solution: For solution click here

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CBSE Class 12 Maths –Chapter 2 Inverse Trigonometric Functions- Study Materials

NCERT Solutions Class 12 All Subjects Sample Papers Past Years Papers

Notes and Study Materials

• Concepts of Inverse Trigonometric Functions
• Master File for Inverse Trigonometric Functions
• Inverse Trigonometric Functions Note
• NCERT Solutions for – Inverse Trigonometric Functions
• NCERT Exemplar Solutions for – Inverse Trigonometric Functions
• Revision Note of Inverse Trigonometric Functions
• R D Sharma Solution of Inverse Trigonometric Functions
• Past Many Years CBSE Questions and Answer Of Relation and Function
• Inverse Trigonometric Functions Mind Map

Examples and Exercise

• Inverse Trigonometric Functions : Practice Paper 1
• Inverse Trigonometric Functions : Practice Paper 2
• Inverse Trigonometric Functions : Practice Paper 3
• Inverse Trigonometric Functions : Practice Paper 4

Inverse Trigonometric Functions: Trigonometric functions are many-one functions but we know that inverse of function exists if the function is bijective. If we restrict the domain of trigonometric functions, then these functions become bijective and the inverse of trigonometric functions are defined within the restricted domain. The inverse of f is denoted by ‘f -1 ‘. Let y = f(x) = sin x, then its inverse is x = sin -1 y.

sin -1 (sinθ) = θ; ∀ θ ∈ \(\left[ \frac { -\pi }{ 2 } ,\frac { \pi }{ 2 } \right]\)

cos -1 (cosθ) = θ; ∀ θ ∈ [0, π]

tan -1 (tanθ) = θ; ∀ θ \(\left[ \frac { -\pi }{ 2 } ,\frac { \pi }{ 2 } \right]\)

cosec -1 (cosecθ) = 0; ∀ θ ∈ \(\left[ \frac { -\pi }{ 2 } ,\frac { \pi }{ 2 } \right]\) , θ ≠ 0

sec -1 (secθ) = θ; ∀ θ ∈ [0, π], θ ≠ \(\frac { \pi }{ 2 }\)

cot -1 (cotθ) = θ; ∀ θ ∈ (0, π)

sin(sin -1 x) = x, ∀ x ∈ [-1, 1]

cos(cos -1 x) = x; ∀ x ∈ [-1, 1]

tan(tan -1 x) = x, ∀ x ∈ R

cosec(cosec -1 x) = x, ∀ x ∈ (-∞, -1] ∪ [1, ∞)

sec(sec -1 x) = x, ∀ x ∈ (-∞, -1] ∪ [1, ∞)

cot(cot -1 x) = x, ∀ x ∈ R

Note: sin -1 (sinθ) = θ ; sin -1 x should not be confused with (sinx) -1 = \(\frac { 1 }{ sinx }\) or sin -1 x = sin -1 (\(\frac { 1 }{ x }\)) land similarly for other trigonometric functions.

The value of an inverse trigonometric function, which lies in the range of principal value branch, is called the principal value of the inverse trigonometric function. Note: Whenever no branch of an inverse trigonometric function is mentioned, it means we have to consider the principal value branch of that function.

Remember Points (i) Sometimes, it may happen, that some of the values of x that we find out does not satisfy the given equation. (ii) While solving an equation, do not cancel the common factors from both sides.

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Case Based Questions (MCQ)

• Miscellaneous

Question 3 - Case Based Questions (MCQ) - Chapter 2 Class 12 Inverse Trigonometric Functions

Last updated at April 16, 2024 by Teachoo

In the school project Sheetal was asked to construct a  triangle and name it as ABC. Two angles A and B were  given to be equal to tan −1 1/3 and tan −1 1/3 respectively

(i) The value of sin A is  _______.

(a) 1/2     (b) 1/3 (c) 1/√5   (d) 2/√5.

cos(A + B + C) =  _______.

(a) 1      (b) 0 (c) −1    (d) 1/2.

If B = cos –1 x, then x =  _______.

(a) 1/√5         (b) 3/√10 (c) 1/√10       (d) 2/√5.

The value of A + B = _______.

(a) π/6       (b) π/4 (c) π/3       (d) π/2.

The third angle, ∠C =  _______.

(a) π/4       (b) π/2 (c) π/3       (d) 3π/4.

Question In the school project Sheetal was asked to construct a triangle and name it as ABC. Two angles A and B were given to be equal to tan−1 1/3 and tan−1 1/3 respectively. Question 1 (i) The value of sin A is _______. (a) 1/2 (b) 1/3 (c) 1/√5 (d) 2/√5 Given that A = tan−1 1/2 tan A = 𝟏/𝟐 Now, we know that 1 + tan2 A = sec2 A 1 + tan2 A = 1/cos^2⁡𝐴 1 + tan2 A = 1/(1 − sin^2⁡𝐴 ) Putting tan A = 1/2 1 + (𝟏/𝟐)^𝟐 = 𝟏/(𝟏 − 〖𝒔𝒊𝒏〗^𝟐⁡𝑨 ) 1 + 1/4 = 1/(1 − sin^2⁡𝐴 ) 5/4 = 1/(1 − sin^2⁡𝐴 ) 1 − sin2 A = 4/5 1 − 4/5 = sin2 A 1/5 = sin2 A sin2 A = 1/5 sin A = 𝟏/√𝟓 So, the correct answer is (C) Question 2 cos(A + B + C) = _______. (A) 1 (B) 0 (C) −1 (D) 1/2 Since ABC is a triangle, By Angle sum property of triangle A + B + C = 180° Thus, cos (A + B + C) = cos 180° = –1 So, the correct answer is (C) Question 3 If B = cos–1 x, then x = _______. (a) 1/√5 (b) 3/√10 (C) 1/√10 (d) 2/√5 Given B = tan−1 1/3 tan B = 1/3 Now, we know that 1 + tan2 B = sec2 B 1 + tan2 B = 1/cos^2⁡𝐵 cos B = 3/√10 B = cos−1 3/√10 Thus, x = 3/√10 So, the correct answer is (B) Question 4 The value of A + B = _______. (a) 𝜋/6 (b) 𝜋/4 (C) 𝜋/3 (d) 𝜋/2 Given A = tan−1 1/2 , B = tan−1 1/3 Now, A + B = tan−1 𝟏/𝟐 + tan−1 𝟏/𝟑 = tan−1 ((1/2 + 1/3)/(1 − 1/2 × 1/3)) = tan−1 (((3 + 2)/(2 × 3))/(1 − 1/6)) = tan−1 ((5/6)/(5/6)) = tan−1 (1) = 𝝅/𝟒 So, the correct answer is (B) Question 5 The third angle, ∠C = _______. (A) 𝜋/4 (B) 𝜋/2 (C) 𝜋/3 (D) 3𝜋/4 Now, A + B = 𝝅/𝟒 And, since ABC is a triangle A + B + C = 180° A + B + C = 𝜋 𝝅/𝟒 + C = 𝜋 C = 𝜋 − 𝜋/4 C = 𝟑𝝅/𝟒 So, the correct answer is (D)

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CBSE Class 12 Maths Case Study Questions With Solutions

CBSE Class 12 Mathematics Case Study Questions are introduced this year in the updated CBSE Board Exam Pattern. According to that this year the candidates need to prepare for the case study problems along with the questions that are legacy of CBSE Board.

In Class XIIth Mathematics Case Study Questions there are problems based on Objective types of questions, Assertions and Reason, and cae based problems. These problems have the intention to examine the students' overall understanding of the subject. If you are preparing for the Maths board exam then this is the right place for you. 

Here, we have provided the complete set of CBSE class 12 maths case study questions With Solutions. These are developed by the subject matter expert. If you want to score good marks in the board papers then you should practice these Case based problems. It is absolutely free of cost. 

Download PDF CBSE Class 12 Maths Case Study From the Given links. It is in chapter wise format.

Class 12th Mathematics Important Formulas, MCQ, Case-Based, Assertion and Reason

Class 12th maths case study.

In class 12th Maths Case Study the questions are based on the real world scenarios. A passage filled with information or data is provided to the students. On the basis of that paragraph upto 5 questions are developed which should be answered by the students. To answer them they need to read the passage carefully and then pay attention to the given data to solve such questions.

These types of problems are generally known as case based questions which can be only solved by referring to the given paragraph.

Class 12 Maths Important Formulas

Knowing about the Maths Important Formulas is a crucial part of solving the Maths questions. Formulas help in solving the problems more efficiently and faster. Therefore the PDF file that we have provided here consists of all the basics and Important formulas of maths. It will help in revisions and solving the questions more accurately and easily.

Every chapter has its own topics and formulas so the PDF has been divided into chapter wise format. And if you access them from this place then you will be able to get all the formulas and other questions separately.

Class 12 Maths Assertion and Reason MCQs

Class 12th Maths Assertion and Reason MCQs PDF with Solutions are also given here. It is the most important part of Case Study Questions because scoring good marks in this section is not that much hard. If your basic concepts are clear. Because most of the time such types of questions are directly prepared by referring to the concepts.

Furthermore, the assertion and reason MCQs are solved by applying the distinct approaches. For instance, to answer these questions first candidates need to verify the Assertion (Statement) and then the reason if both are correct, then learners need to verify whether both statement and reason support each other or not.

There are a total of 5 sections in CBSE Class 12 Maths Questions Term 1. Section A contains 1 mark, Section B contains 2 marks, Section C contains 3 marks, Section D contains 4 marks and the last Section E contains 5 marks. A total of 5 questions are given in these sections.

No, In Term 1 exam there will be a total of 5 questions in each case study of class 12 maths, out of which 4 are compulsory to solve.

CBSE 12th 2024-25 : Biology Official Competency Focused Practice Questions released by CBSE

CBSE 12th 2024-25 : Mathematics Official Competency Focused Practice Questions released by CBSE

CBSE Board Class 12 Computer Science Answer Key 2024 and Question Papers, Download PDF All SETs

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CBSE Board Class 12 History Answer Key 2024 and Question Papers, Download PDF All SETs

CBSE Board 12th History Exam 2024 : Chapterwise Most Important Question with Answers

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Inverse Trigonometric Functions For Class 12

Inverse Trigonometric Functions for Class 12 includes the major concepts related to the inverse of trigonometric functions, which will help the students score good marks in their examinations. The inverse trigonometric functions play an essential role in calculus, for they serve to define many integrals. The concepts of inverse trigonometric functions are also used in science and engineering.

In this chapter, you will learn about the restrictions on domains and ranges of trigonometric functions, which assure the existence of their inverses and observe their behaviour through graphical representations. Besides, students can also learn some elementary properties of inverse trigonometric functions.

Click here to get the Notes for all chapters of Class 12 Maths .

Inverse Trigonometric Functions Class 12 Concepts

The concepts covered in this Class 12 Chapter 2 Inverse Trigonometric Functions are:

• Introduction
• Basic Concepts

Properties of Inverse Trigonometric Functions

Inverse trigonometric functions class 12 notes.

Basics Concepts

Let’s recall the domain and range of trigonometric functions.

tangent function, i.e., tan : R – { x : x = (2n + 1)π/2, n ∈ Z} →R

cotangent function, i.e., cot : R – { x : x = nπ, n ∈ Z} →R

secant function, i.e., sec : R – { x : x = (2n + 1)π/2, n ∈ Z} →R – (– 1, 1)

cosecant function, i.e., cosec : R – { x : x = nπ, n ∈ Z} →R – (– 1, 1)

The below table gives the inverse trigonometric function (principal value branches) along with their domains and ranges.

Some properties of inverse trigonometric functions are listed below:

sin −1 (1/x) = cosec −1 x, x ≥ 1 or x ≤ −1

cos −1 (1/x) = sec −1 x, x ≥ 1 or x ≤ −1

tan −1 (1/x) = cot –1 x, x > 0

(ii) tan –1 (–x) = – tan –1 x, x ∈ R

(iii) cosec –1 (–x) = – cosec –1 x, | x | ≥ 1

(ii) sec –1 (–x) = π – sec –1 x, | x | ≥ 1

(iii) cot –1 (–x) = π – cot –1 x, x ∈ R

(ii) tan –1 x + cot –1 x = π/2, x ∈ R

(iii) cosec –1 x + sec –1 x = π/2, |x| ≥ 1

Click here to get more information about inverse trigonometric functions properties .

Video Lesson on Trigonometry

Inverse Trigonometric Functions Class 12 Questions

1. Find the principal value of tan -1 (-√3).

2. Find the value of cos -1 (1/2) + 2 sin -1 (1/2).

3. Prove that tan -1 (2/11) + tan -1 (7/24) = tan -1 (1/2).

5. Solve the equation: 2tan –1 (cos x) = tan –1 (2 cosec x)

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Class 12 Maths Chapter 2 – Inverse Trigonometric Functions

Inverse Trigonometric Functions – Introduction

In Chapter 1 , we have studied the inverse of function f, which is denoted from f-1, exists if f is monotonous and covering. There are many tasks that are not one or the other, covering or both and, therefore, we cannot talk about their inverse. In class XI, we studied that trigonometric functions are not monotonous and are on their natural domains and campuses and hence their inversions do not exist.

In this chapter, we will study restrictions on the domains and categories of trigonometric functions that ensure the existence of their inverses and observe their behavior through graphical representation. In addition, some of the primary qualities will also be discussed. Inverse trigonometric functions play an important role in calculus as they define many integrals. The concept of inverse trigonometric functions is also used in science and engineering.

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• CBSE Class 12 Maths Chapter-2 Inverse Trigonometric Functions Formula

Inverse Trigonometric Functions Formula for CBSE Class 12 Maths - Free PDF Download

Inverse Trigonometric Formulas are part of Trigonometry which is further an element of geometry. Inverse trigonometric functions formulas enable us to learn about the association between sides and angles of a right-angled triangle. In Class 11 and 12, you will come across inverse trigonometric functions formulas list Class 12 PDF, based on the ratios and functions such as sin, cos, and tan. In the same manner, the inverse trigonometric functions are expressed as sin -1 x, cos -1 x, tan -1 x, cot -1 x, sec -1 x, cosec -1 x.

Inverse Trigonometric Functions Formulas List

Now, let us get the formulas linked with these functions. In order to solve different types of inverse trigonometric functions, inverse trigonometry formulas are extracted from some basic properties of trigonometry. Inverse trigonometric function formula list is provided below for reference to solve the problems.

Inverse Trigonometric Functions Formulas

Inverse trigonometric formulas class 12.

List class CBSE Class 12 Trigonometry Formulas mathematics contains Inverse Trigonometric formulas for Class 12. This chapter includes the definition, inverse trigonometry formula, graphs and elementary properties of inverse trigonometric functions. Trigonometry Formulas for Class 12 play a key role in these chapters. Thus, all trigonometry formulas are given here.

Basic Concepts Included in Trigonometry Formulas For Class 12

Below are the basic trigonometric functions based on the domain and range

Basic Trigonometric Functions Based on the Domain and Range

FAQs on CBSE Class 12 Maths Chapter-2 Inverse Trigonometric Functions Formula

1. What is meant by Inverse Trigonometric Function?

The inverse trigonometric functions are called anti trigonometric functions or sometimes known as the cyclometric functions or arcus functions. The inverse trigonometric functions of sine, cosine, tangent, secant, cosecant, and cotangent are used to determine the angle of a triangle from any of the trigonometric functions.

2. What are the applications of Inverse Trigonometric Function?

It is widely used in different fields including geometry, physics, engineering etc. But in general, the convention symbol to indicate the inverse trigonometric function with the help of arc-prefix such as arcsin(x), arccos(x), arctan(x), arccsc(x), arcsec(x), arccot(x). In order to identify the sides of a triangle when the remaining side lengths are known.

Take into the function y = f(x), and x = g(y) then the inverse function is expressed as g = f -1 ,

This implies that if y=f(x), then x = f -1 (y).

In a way that f(g(y))=y and g(f(y))=x.

Example of Inverse trigonometric functions: x= sin -1 y

3. What are the properties of inverse trigonometric functions?

Below is the inverse trigonometric function formula:

sin -1 (1/a) = cosec -1 (a), a ≥ 1 or a ≤ – 1

sin -1 (–a) = – sin -1 (a), a ∈ [– 1, 1]

cos -1 (1/a) = sec -1 (a), a ≥ 1 or a ≤ – 1

cos -1 (–a) = π – cos -1 (a), a ∈ [– 1, 1]

tan -1 (1/a) = cot -1 (a), a>0

tan -1 (–a) = – tan -1 (a), a ∈ R

sec -1 (–a) = π – sec -1 (a), | a | ≥ 1

cosec -1 (–a) = –cosec -1 (a), | a | ≥ 1

cot -1 (–a) = π – cot -1 (a), a ∈ R

CBSE Class 12 Maths Formulas

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