trigonometry case study questions class 11

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Class 11 Mathematics Case Study Questions

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The rationale behind teaching Mathematics

The general rationale to teach Mathematics at the senior secondary level is to assist students:

In knowledge acquisition and cognitive understanding of basic ideas, words, principles, symbols, and mastery of underlying processes and abilities, notably through motivation and visualization.
To experience the flow of arguments while demonstrating a point or addressing an issue.
To use the information and skills gained to address issues using several methods wherever possible.
To cultivate a good mentality in order to think, evaluate, and explain coherently.
To spark interest in the subject by taking part in relevant tournaments.
To familiarise pupils with many areas of mathematics utilized in daily life.
To pique students’ interest in studying mathematics as a discipline.

Case studies in Class 11 Mathematics

A case study in mathematics is a comprehensive examination of a specific mathematical topic or scenario. Case studies are frequently used to investigate the link between theory and practise, as well as the connections between different fields of mathematics. A case study will frequently focus on a specific topic or circumstance and will investigate it using a range of methodologies. These approaches may incorporate algebraic, geometric, and/or statistical analysis.

Sample Class 11 Mathematics case study questions

When it comes to preparing for Class 11 Mathematics, one of the best things Class 11 Mathematics students can do is to look at some Class 11 Mathematics sample case study questions. Class 11 Mathematics sample case study questions will give you a good idea of the types of Class 11 Mathematics sample case study questions that will be asked in the exam and help you to prepare more effectively.

Looking at sample questions is also a good way to identify any areas of weakness in your knowledge. If you find that you struggle with a particular topic, you can then focus your revision on that area.

myCBSEguide offers ample Class 11 Mathematics case study questions, so there is no excuse. With a little bit of preparation, Class 11 Mathematics students can boost their chances of getting the grade they deserve.

Some samples of Class 11 Mathematics case study questions are as follows:

Class 11 Mathematics case study question 1

9 km and 13 km
9.8 km and 13.8 km
9.5 km and 13.5 km
10 km and 14 km
x ≤ −1913
x < −1613
−1613 < x < −1913
There are no solution.
y ≤ 12 x+2
y > 12 x+2
y ≥ 12 x+2
y < 12 x+2

Answer Key:

(b) 9.8 km and 13.8 km
(a) −1913 ≤ x
(b) y > 12 x+2
(d) (-5, 5)

Class 11 Mathematics case study question 2

2 C 1 × 13 C 10
2 C 1 × 10 C 13
1 C 2 × 13 C 10
2 C 10 × 13 C 10
6 C 2 × 3 C 4 × 11 C 5
6 C 2 × 3 C 4 × 11 C 5
6 C 2 × 3 C 5 × 11 C 4
6 C 2 × 3 C 1 × 11 C 5
(b) (13) 4 ways
(c) 2860 ways.

Class 11 Mathematics case study question 3

Read the Case study given below and attempt any 4 sub parts: Father of Ashok is a builder, He planned a 12 story building in Gurgaon sector 5. For this, he bought a plot of 500 square yards at the rate of Rs 1000 /yard². The builder planned ground floor of 5 m height, first floor of 4.75 m and so on each floor is 0.25 m less than its previous floor.

Class 11 Mathematics case study question 4

Read the Case study given below and attempt any 4 sub parts: villages of Shanu and Arun’s are 50km apart and are situated on Delhi Agra highway as shown in the following picture. Another highway YY’ crosses Agra Delhi highway at O(0,0). A small local road PQ crosses both the highways at pints A and B such that OA=10 km and OB =12 km. Also, the villages of Barun and Jeetu are on the smaller high way YY’. Barun’s village B is 12km from O and that of Jeetu is 15 km from O.

Now answer the following questions:

5x + 6y = 60
6x + 5y = 60
(a) (10, 0)
(b) 6x + 5y = 60
(b) 60/√ 61 km
(d) 2√61 km

A peek at the Class 11 Mathematics curriculum

The Mathematics Syllabus has evolved over time in response to the subject’s expansion and developing societal requirements. The Senior Secondary stage serves as a springboard for students to pursue higher academic education in Mathematics or professional subjects such as Engineering, Physical and Biological Science, Commerce, or Computer Applications. The current updated curriculum has been prepared in compliance with the National Curriculum Framework 2005 and the instructions provided by the Focus Group on Teaching Mathematics 2005 in order to satisfy the rising demands of all student groups. Greater focus has been placed on the application of various principles by motivating the themes from real-life events and other subject areas.

Class 11 Mathematics (Code No. 041)

Design of Class 11 Mathematics exam paper

CBSE Class 11 mathematics question paper is designed to assess students’ understanding of the subject’s essential concepts. Class 11 mathematics question paper will assess their problem-solving and analytical abilities. Before beginning their test preparations, students in Class 11 maths should properly review the question paper format. This will assist Class 11 mathematics students in better understanding the paper and achieving optimum scores. Refer to the Class 11 Mathematics question paper design provided.

Class 11 Mathematics Question Paper Design

No chapter-wise weightage. Care to be taken to cover all the chapters.
Suitable internal variations may be made for generating various templates keeping the overall weightage to different forms of questions and typology of questions the same.

Choice(s): There will be no overall choice in the question paper. However, 33% of internal choices will be given in all the sections.

Prescribed Books:

Mathematics Textbook for Class XI, NCERT Publications
Mathematics Exemplar Problem for Class XI, Published by NCERT
Mathematics Lab Manual class XI, published by NCERT

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Competency Based Learning in CBSE Schools
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CBSE Class 11 Maths – Chapter 3 Trigonometric Functions- Study Materials

NCERT Solutions Class 11 All Subjects Sample Papers Past Years Papers

Sets : Notes and Study Materials -pdf

Concepts of Trigonometric Functions
Trigonometric Functions Master File
Trigonometric Functions Revision Notes
R D Sharma Solution of Trigonometric Functions
NCERT Solution Trigonometric Functions
NCERT Exemplar Solution Trigonometric Functions
Trigonometric Functions : Solved Example 1

CBSE Class 11 Maths Notes Chapter 3 Trigonometric Functions

Angle Angle is a measure of rotation of a given ray about its initial point. The original ray is called the initial side and the final position of ray after rotation is called terminal side of the angle. The point of rotation is called vertex. If the direction of rotation is anti-clockwise, the angle is said to be positive and if the direction of rotation is clockwise, then the angle is negative.

Measuring Angles There are two systems of measuring angles Sexagesimal system (degree measure): If a rotation from the initial side to terminal side is ( 1 360 ) t h of a revolution, the angle is said to have a measure of one degree, written as 1°. One sixtieth of a degree is called a minute, written as 1′ and one-sixtieth of a minute is called a second, written as 1″ Thus, 1° = 60′ and 1′ = 60″

Circular system (radian measure): A radian is an angle subtended at the centre of a circle by an arc, whose length is equal to the radius of the circle. We denote 1 radian by 1°.

Relation Between Radian and Degree We know that a complete circle subtends at its centre an angle whose measure is 2π radians as well as 360°. 2π radian = 360°. Hence, π radian = 180° or 1 radian = 57° 16′ 21″ (approx) 1 degree = 0.01746 radian

Six Fundamental Trigonometric Identities

sinx = 1 c o s e c x
cos x = 1 s e c x
tan x = 1 c o t x
sin 2 x + cos 2 x = 1
1 + tan 2 x = sec 2 x
1 + cot 2 x = cosec 2 x

Trigonometric Functions – Class 11 Maths Notes

Trigonometric ratios are defined for acute angles as the ratio of the sides of a right angled triangle. The extension of trigonometric ratios to any angle in terms of radian measure (real number) are called trigonometric function. The signs of trigonometric function in different quadrants have been given in following table.

Domain and Range of Trigonometric Functions

Sine, Cosine, and Tangent of Some Angles Less Than 90°

Allied or Related Angles The angles n π 2 ± θ are called allied or related angle and θ ± n × (2π) are called coterminal angles. For general reduction, we have following rules, the value of trigonometric function for ( n π 2 ± θ ) is numerically equal to

the value of the same function, if n is an even integer with the algebraic sign of the function as per the quadrant in which angle lies.
the corresponding co-function of θ, if n is an odd integer with the algebraic sign of the function for the quadrant in which it lies, here sine and cosine, tan and cot, sec and cosec are cofunctions of each other.

Functions of Negative Angles

For any acute angle of θ. We have,

sin(-θ) = – sinθ
cos (-θ) = cosθ
tan (-θ) = – tanθ
cot (-θ) = – cotθ
sec (-θ) = secθ
cosec (-θ) = – cosecθ

Some Formulae Regarding Compound Angles

An angle made up of the sum or difference of two or more angles is called compound angles. The basic results in direction are called trigonometric identities as given below: (i) sin (x + y) = sin x cos y + cos x sin y (ii) sin (x – y) = sin x cos y – cos x sin y (iii) cos (x + y) = cos x cos y – sin x sin y (iv) cos (x – y) = cos x cos y + sin x sin y

(ix) sin(x + y) sin (x – y) = sin 2 x – sin 2 y = cos 2 y – cos 2 x (x) cos (x + y) cos (x – y) = cos 2 x – sin 2 y = cos 2 y – sin 2 x

Transformation Formulae

2 sin x cos y = sin (x + y) + sin (x – y)
2 cos x sin y = sin (x + y) – sin (x – y)
2 cos x cos y = cos (x + y) + cos (x – y)
2 sin x sin y = cos (x – y) – cos (x + y)
sin x + sin y = 2 sin( x + y 2 ) cos( x − y 2 )
sin x – sin y = 2 cos( x + y 2 ) sin( x − y 2 )
cos x + cos y = 2 cos( x + y 2 ) cos( x − y 2 )
cos x – cos y = -2 sin( x + y 2 ) sin( x − y 2 )

Trigonometric Ratios of Multiple Angles

Product of Trigonometric Ratios

sin x sin (60° – x) sin (60° + x) = 1 4 sin 3x
cos x cos (60° – x) cos (60° + x) = 1 4 cos 3x
tan x tan (60° – x) tan (60° + x) = tan 3x
cos 36° cos 72° = 1 4
cos x . cos 2x . cos 2 2 x . cos 2 3 x … cos 2 n-1 = s i n 2 n x 2 n s i n x

Sum of Trigonometric Ratio, if Angles are in A.P.

Trigonometric Equations Equation which involves trigonometric functions of unknown angles is known as the trigonometric equation.

Solution of a Trigonometric Equation A solution of a trigonometric equation is the value of the unknown angle that satisfies the equation. A trigonometric equation may have an infinite number of solutions.

Principal Solution The solutions of a trigonometric equation for which 0 ≤ x ≤ 2π are called principal solutions.

General Solutions A solution of a trigonometric equation, involving ‘n’ which gives all solution of a trigonometric equation is called the general solutions.

General Solutions of Trigonometric Equation

sin x = 0 ⇔ x = nπ, n ∈ Z
cos x = 0 ⇔ x = (2n + 1) π 2 , n ∈ Z
tan x = 0 ⇔ x = nπ, n ∈ Z
sin x = sin y ⇔ x = nπ + (-1) n y, n ∈ Z
cos x = cos y ⇔ x = 2nπ ± y, n ∈ Z
tan x = tan y ⇔ x = nπ ± y, n ∈ Z
sin 2 x = sin 2 y ⇔ x = nπ ± y, n ∈ Z
cos 2 x = cos 2 y ⇔ x = nπ ± y, n ∈ Z
tan 2 x = tan 2 y ⇔ x = nπ ± y, n ∈ Z

Basic Rules of Triangle

In a triangle ABC, the angles are denoted by capital letters A, B and C and the lengths of sides of opposite to these angles are denoted by small letters a, b and c, respectively. Sine Rule s i n A a = s i n B b = s i n C c

Cosine Rule a 2 = b 2 + c 2 – 2bc cos A b 2 = c 2 + a 2 – 2ac cos B c 2 = a 2 + b 2 – 2ab cos C

Projection Rule a = b cos C + c cos B b = c cos A + a cos C c = a cos B + b cos A

Trigonometric Functions Class 11 MCQs Questions with Answers

Question 1. The value of cos² x + cos² y – 2cos x × cos y × cos (x + y) is (a) sin (x + y) (b) sin² (x + y) (c) sin³ (x + y) (d) sin 4 (x + y)

Answer: (b) sin² (x + y) Hint: cos² x + cos² y – 2cos x × cos y × cos(x + y) {since cos(x + y) = cos x × cos y – sin x × sin y } = cos² x + cos² y – 2cos x × cos y × (cos x × cos y – sin x × sin y) = cos² x + cos² y – 2cos² x × cos² y + 2cos x × cos y × sin x × sin y = cos² x + cos² y – cos² x × cos² y – cos² x × cos² y + 2cos x × cos y × sin x × sin y = (cos² x – cos² x × cos² y) + (cos² y – cos² x × cos² y) + 2cos x × cos y × sin x × sin y = cos² x(1- cos² y) + cos² y(1 – cos² x) + 2cos x × cos y × sin x × sin y = sin² y × cos² x + sin² x × cos² y + 2cos x × cos y × sin x × sin y (since sin² x + cos² x = 1 ) = sin² x × cos² y + sin² y × cos² x + 2cos x × cos y × sin x × sin y = (sin x × cos y)² + (sin y × cos x)² + 2cos x × cos y × sin x × sin y = (sin x × cos y + sin y × cos x)² = {sin (x + y)}² = sin² (x + y)

Question 2. If a×cos x + b × cos x = c, then the value of (a × sin x – b²cos x)² is (a) a² + b² + c² (b) a² – b² – c² (c) a² – b² + c² (d) a² + b² – c²

Answer: (d) a² + b² – c² Hint: We have (a×cos x + b × sin x)² + (a × sin x – b × cos x)² = a² + b² ⇒ c² + (a × sin x – b × cos x)² = a² + b² ⇒ (a × sin x – b × cos x)² = a² + b² – c²

Question 3. If cos a + 2cos b + cos c = 2 then a, b, c are in (a) 2b = a + c (b) b² = a × c (c) a = b = c (d) None of these

Answer: (a) 2b = a + c Hint: Given, cos A + 2 cos B + cos C = 2 ⇒ cos A + cos C = 2(1 – cos B) ⇒ 2 cos((A + C)/2) × cos((A-C)/2 = 4 sin²(B/2) ⇒ 2 sin(B/2)cos((A-C)/2) = 4sin² (B/2) ⇒ cos((A-C)/2) = 2sin (B/2) ⇒ cos((A-C)/2) = 2cos((A+C)/2) ⇒ cos((A-C)/2) – cos((A+C)/2) = cos((A+C)/2) ⇒ 2sin(A/2)sin(C/2) = sin(B/2) ⇒ 2{√(s-b)(s-c)√bc} × {√(s-a)(s-b)√ab} = √(s-a)(s-c)√ac ⇒ 2(s – b) = b ⇒ a + b + c – 2b = b ⇒ a + c – b = b ⇒ a + c = 2b

Question 4. The value of cos 5π is (a) 0 (b) 1 (c) -1 (d) None of these

Answer: (c) -1 Hint: Given, cos 5π = cos (π + 4π) = cos π = -1

Question 5. In a triangle ABC, cosec A (sin B cos C + cos B sin C) equals (a) none of these (b) c/a (c) 1 (d) a/c

Answer: (c) 1 Hint: Given cosec A (sin B cos C + cos B sin C) = cosec A × sin(B+C) = cosec A × sin(180 – A) = cosec A × sin A = cosec A × 1/cosec A = 1

Question 6. If the angles of a triangle be in the ratio 1 : 4 : 5, then the ratio of the greatest side to the smallest side is (a) 4 : (√5 – 1) (b) 5 : 4 (c) (√5 – 1) : 4 (d) none of these

Answer: (a) 4 : (√5 – 1) Hint: Given, the angles of a triangle be in the ratio 1 : 4 : 5 ⇒ x + 4x + 5x = 180 ⇒ 10x = 180 ⇒ x = 180/10 ⇒ x = 18 So, the angle are: 18, 72, 90 Since a : b : c = sin A : sin B : sin C ⇒ a : b : c = sin 18 : sin 72 : sin 90 ⇒ a : b : c = (√5 – 1)/4 : {√(10 + 2√5)}/4 : 1 ⇒ a : b : c = (√5 – 1) : {√(10 + 2√5)} : 4 Now, c /a = 4/(√5 – 1) ⇒ c : a = 4 : (√5 – 1)

Question 7. The value of cos 180° is (a) 0 (b) 1 (c) -1 (d) infinite

Answer: (c) -1 Hint: 180 is a standard degree generally we all know their values but if we want to go theoretically then cos(90 + x) = – sin(x) So, cos 180 = cos(90 + 90) = -sin 90 = -1 {sin 90 = 1} So, cos 180 = -1

Question 8. The perimeter of a triangle ABC is 6 times the arithmetic mean of the sines of its angles. If the side b is 2, then the angle B is (a) 30° (b) 90° (c) 60° (d) 120°

Answer: (b) 90° Hint: Let the lengths of the sides if ∆ABC be a, b and c Perimeter of the triangle = 2s = a + b + c = 6(sinA + sinB + sinC)/3 ⇒ (sinA + sinB + sinC) = ( a + b + c)/2 ⇒ (sinA + sinB + sinC)/( a + b + c) = 1/2 From sin formula,Using sinA/a = sinB/b = sinC/c = (sinA + sinB + sinC)/(a + b + c) = 1/2 Now, sinB/b = 1/2 Given b = 2 So, sinB/2 = 1/2 ⇒ sinB = 1 ⇒ B = π/2

Question 9: If 3 × tan(x – 15) = tan(x + 15), then the value of x is (a) 30 (b) 45 (c) 60 (d) 90

Answer: (b) 45 Hint: Given, 3×tan(x – 15) = tan(x + 15) ⇒ tan(x + 15)/tan(x – 15) = 3/1 ⇒ {tan(x + 15) + tan(x – 15)}/{tan(x + 15) – tan(x – 15)} = (3 + 1)/(3 – 1) ⇒ {tan(x + 15) + tan(x – 15)}/{tan(x + 15) – tan(x – 15)} = 4/2 ⇒ {tan(x + 15) + tan(x – 15)}/{tan(x + 15) – tan(x – 15)} = 2 ⇒ sin(x + 15 + x – 15)/sin(x + 15 – x + 15) = 2 ⇒ sin 2x/sin 30 = 2 ⇒ sin 2x/(1/2) = 2 ⇒ 2 × sin 2x = 2 ⇒ sin 2x = 1 ⇒ sin 2x = sin 90 ⇒ 2x = 90 ⇒ x = 45

Question 10. If the sides of a triangle are 13, 7, 8 the greatest angle of the triangle is (a) π/3 (b) π/2 (c) 2π/3 (d) 3π/2

Answer: (c) 2π/3 Hint: Given, the sides of a triangle are 13, 7, 8 Since greatest side has greatest angle, Now Cos A = (b² + c² – a²)/2bc ⇒ Cos A = (7² + 8² – 13²)/(2×7×8) ⇒ Cos A = (49 + 64 – 169)/(2×7×8) ⇒ Cos A = (113 – 169)/(2×7×8) ⇒ Cos A = -56/(2×56) ⇒ Cos A = -1/2 ⇒ Cos A = Cos 2π/3 ⇒ A = 2π/3 So, the greatest angle is = 2π/3

Question 11. The value of tan 20 × tan 40 × tan 80 is (a) tan 30 (b) tan 60 (c) 2 tan 30 (d) 2 tan 60

Answer: (b) tan 60 Hint: Given, tan 20 × tan 40 × tan 80 = tan 40 × tan 80 × tan 20 = [{sin 40 × sin 80}/{cos 40 × cos 80}] × (sin 20/cos 20) = [{2 * sin 40 × sin 80}/{2 × cos 40 × cos 80}] × (sin 20/cos 20) = [{cos 40 – cos 120}/{cos 120 + cos 40}] × (sin 20/cos 20) = [{cos 40 – cos (90 + 30)}/{cos (90 + 30) + cos 40}] × (sin 20/cos 20) = [{cos 40 + sin30}/{-sin30 + cos 40}] × (sin 20/cos 20) = [{(2 × cos 40 + 1)/2}/{(-1 + cos 40)/2}] × (sin 20/cos 20) = [{2 × cos 40 + 1}/{-1 + cos 40}] × (sin 20/cos 20) = [{2 × cos 40 × sin 20 + sin 20}/{-cos 20 + cos 40 × cos 20}] = (sin 60 – sin 20 + sin 20)/(-cos 20 + cos 60 + cos 20) = sin 60/cos 60 = tan 60 So, tan 20 × tan 40 × tan 80 = tan 60

Question 12. If the angles of a triangle be in the ratio 1 : 4 : 5, then the ratio of the greatest side to the smallest side is (a) 4 : (√5 – 1) (b) 5 : 4 (c) (√5 – 1) : 4 (d) none of these

Question 13. The general solution of √3 cos x – sin x = 1 is (a) x = n × π + (-1)n × (π/6) (b) x = π/3 – n × π + (-1)n × (π/6) (c) x = π/3 + n × π + (-1)n × (π/6) (d) x = π/3 – n × π + (π/6)

Answer: (c) x = π/3 + n × π + (-1)n × (π/6) Hint: √3 cos x-sin x=1 ⇒ (√3/2)cos x – (1/2)sin x = 1/2 ⇒ sin 60 × cos x – cos 60 × sin x = 1/2 ⇒ sin (x – 60) = 1/2 ⇒ sin (x – π/3) = sin 30 ⇒ sin (x – π/3) = sinπ/6 ⇒ x – π/3 = n × π + (-1)n × (π/6) {where n ∈ Z} ⇒ x = π/3 + n × π + (-1)n × (π/6)

Question 14. If tan² θ = 1 – e², then the value of sec θ + tan³ θ × cosec θ is (a) 2 – e² (b) (2 – e²) 1/2 (c) (2 – e²)² (d) (2 – e²) 3/2

MCQ Questions for Class 11 Maths Chapter 3 Trigonometric Functions with Answers 1

Question 15. The value of cos 20 + 2sin² 55 – √2 sin65 is (a) 0 (b) 1 (c) -1 (d) None of these

Answer: (b) 1 Hint: Given, cos 20 + 2sin² 55 – √2 sin65 = cos 20 + 1 – cos 110 – √2 sin65 {since cos 2x = 1 – 2sin² x} = 1 + cos 20 – cos 110 – √2 sin65 = 1 – 2 × sin {(20 + 110)/2 × sin{(20 – 110)/2} – √2 sin65 {Apply cos C – cos D formula} = 1 – 2 × sin 65 × sin (-45) – √2 sin65 = 1 + 2 × sin 65 × sin 45 – √2 sin65 = 1 + (2 × sin 65)/√2 – √2 sin65 = 1 + √2 ( sin 65 – √2 sin 65 = 1 So, cos 20 + 2sin² 55 – √2 sin65 = 1

Question 16. If the radius of the circumcircle of an isosceles triangle PQR is equal to PQ ( = PR), then the angle P is (a) 2π/3 (b) π/3 (c) π/2 (d) π/6

Answer: (a) 2π/3 Hint: Let S be the center of the circumcircle of triangle PQR. So, SP = SQ = SR = PQ = PR, where SP, SQ & SR are radii. Thus SPQ & SPR are equilateral triangles. ⇒ ∠QSP = 60°; Similarly ∠RQP = 60° ⇒ Angle at the center QSP = 120° So, SRPQ is a rhombus, since all the four sides are equal. Hence, its opposite angles are equal; so ∠P = ∠QSP = 120°

Question 17. If cos a + 2cos b + cos c = 2 then a, b, c are in (a) 2b = a + c (b) b² = a × c (c) a = b = c (d) None of these

Answer: (a) 2b = a + c Hint: Given, cos A + 2 cos B + cos C = 2 ⇒ cos A + cos C = 2(1 – cos B) ⇒ 2 cos((A + C)/2) × cos((A-C)/2 = 4 sin² (B/2) ⇒ 2 sin(B/2)cos((A-C)/2) = 4sin² (B/2) ⇒ cos((A-C)/2) = 2sin (B/2) ⇒ cos((A-C)/2) = 2cos((A+C)/2) ⇒ cos((A-C)/2) – cos((A+C)/2) = cos((A+C)/2) ⇒ 2sin(A/2)sin(C/2) = sin(B/2) ⇒ 2{√(s-b)(s-c)√bc} × {√(s-a)(s-b)√ab} = √(s-a)(s-c)√ac ⇒ 2(s – b) = b ⇒ a + b + c – 2b = b ⇒ a + c – b = b ⇒ a + c = 2b

Question 18. The value of 4 × sin x × sin(x + π/3) × sin(x + 2π/3) is (a) sin x (b) sin 2x (c) sin 3x (d) sin 4x

Answer: (c) sin 3x Hint: Given, 4 × sin x × sin(x + π/3) × sin(x + 2π/3) = 4 × sin x × {sin x × cos π/3 + cos x × sin π/3} × {sin x × cos 2π/3 + cos x × sin 2π/3} = 4 × sin x × {(sin x)/2 + (√3 × cos x)/2} × {-(sin x)/2 + (√3 × cos x)/2} = 4 × sin x × {-(sin 2x)/4 + (3 × cos 2x)/4} = sin x × {-sin 2x + 3 × cos 2x} = sin x × {-sin 2x + 3 × (1 – sin 2x)} = sin x × {-sin 2x + 3 – 3 × sin 2x} = sin x × {3 – 4 × sin 2x} = 3 × sin x – 4 sin 3x = sin 3x So, 4 × sin x × sin(x + π/3) × sin(x + 2π/3) = sin 3x

Question 19. If tan A – tan B = x and cot B – cot A = y, then the value of cot (A – B) is (a) x + y (b) 1/x + y (c) x + 1/y (d) 1/x + 1/y

Answer: (d) 1/x + 1/y Hint: Given, tan A – tan B = x ……………. 1 and cot B – cot A = y ……………. 2 From equation, 1/cot A – 1/cot B = x ⇒ (cot B – cot A)/(cot A × cot B) = x ⇒ y/(cot A × cot B) = x {from equation 2} ⇒ y = x × (cot A × cot B) ⇒ cot A × cot B = y/x Now, cot (A – B) = (cot A × cot B + 1)/(cot B – cot A) ⇒ cot (A – B) = (y/x + 1)/y ⇒ cot (A – B) = (y/x) × (1/y) + 1/y ⇒ cot (A – B) = 1/x + 1/y

Question 20. The value of (sin 7x + sin 5x) /(cos 7x + cos 5x) + (sin 9x + sin 3x) / (cos 9x + cos 3x) is (a) tan 6x (b) 2 tan 6x (c) 3 tan 6x (d) 4 tan 6x

Answer: (b) 2 tan 6x Hint: Given, (sin 7x + sin 5x) /(cos 7x + cos 5x) + (sin 9x + sin 3x) / (cos 9x + cos 3x) ⇒ [{2 × sin(7x+5x)/2 × cos(7x-5x)/2}/{2 × cos(7x+5x)/2 × cos(7x-5x)/2}] + [{2 × sin(9x+3x)/2 × cos(9x-3x)/2}/{2 × cos(9x+3x)/2 × cos(9x-3x)/2}] ⇒ [{2 × sin 6x × cosx}/{2 × cos 6x × cosx}] + [{2 × sin 6x × cosx}/{2 × cos 6x × cosx}] ⇒ (sin 6x/cos 6x) + (sin 6x/cos 6x) ⇒ tan 6x + tan 6x ⇒ 2 tan 6x

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Chapter 3 Class 11 Trigonometric Functions

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NCERT Solutions of Chapter 3 Class 11 Trigonometry is available free at teachoo. You can check the detailed explanation of all questions of exercises, examples and miscellaneous by clicking on the Exercise link below.

We had learned Basics of Trigonometry in Class 10. In this chapter, we will learn

What is a positive or a negative angle
Measuring angles in Degree , Minutes and Seconds
Radian measure of an angle
Converting Degree to Radians , and vice-versa
Sign of sin, cos, tan in all 4 quadrants
Finding values of trigonometric functions when one value is given (Example: Finding value of sin, cot, cosec, tan, sec, when cos x = -3/5 is given)
Finding Value of trigonometric functions, given angle
Solving questions by formula like (x + y) formula, 2x 3x formula, Cos x + cos y formula , 2 sin x sin y formula
Finding principal and general solutions of a trigonometric equation
Sin and Cosine Formula with supplementary Questions

Important questions are marked, and Formula sheet is also provided. Click on an exercise or topic to begin.

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NCERT Solutions Class 11 Maths Chapter 3 Trigonometric Functions

NCERT Solutions for Class 11 Maths Chapter 3 Trigonometric Functions are formulated to explain the fundamental application of trigonometric formulas and the graphs of their functions. Trigonometry is an important part of Class 11 maths that involves studying various relations between sides and angles of triangles . Trigonometric Functions are applied to define these relations and have numerous applications in various other fields, including science and engineering. They are often used for basic geometric calculations and to explain numeric solutions. The knowledge of Trigonometric Functions is vital for subjects like astronomy and geography. NCERT Solutions Class 11 Maths Chapter 3 will offer the right foundational skills in students to study trigonometric relations and functions along with their practical applications.

Chapter 3 of Class 11 Maths will enable students to generalize the concept of trigonometric ratios to trigonometric functions. Learning about the properties of Trigonometric Functions and operations based on them is crucial for math studies. With the regular practice of Class 11 Maths NCERT Solutions Chapter 3, students will quickly master the solutions to equations using Trigonometric Functions. The wide range of problems and examples provided in these solutions are beneficial in promoting an in-depth understanding of concepts. To learn and practice with NCERT Solutions Chapter 3 Trigonometric Functions, download the exercises provided in the links below.

NCERT Solutions Class 11 Maths Chapter 3 Ex 3.1
NCERT Solutions Class 11 Maths Chapter 3 Ex 3.2
NCERT Solutions Class 11 Maths Chapter 3 Ex 3.3
NCERT Solutions Class 11 Maths Chapter 3 Ex 3.4
NCERT Solutions Class 11 Maths Chapter 3 Miscellaneous Ex

NCERT Solutions for Class 11 Maths Chapter 3 PDF

Trigonometry sees the use of many formulas, theorems, and steps to solve the sums hence, ensuring that kids allot an ample amount of time for practice is very important. NCERT Solutions for Class 11 Maths Chapter 3 are proficiently modeled to support higher-level math learning. The comprehensive format of these solutions is highly reliable to enhance problem-solving skills in engaging ways. To learn and practice trigonometric functions with these solutions, click on the links of the pdf file given below.

☛ Download Class 11 Maths NCERT Solutions Chapter 3 Trigonometric Functions

NCERT Class 11 Maths Chapter 3 Download PDF

NCERT Solutions Class 11 Maths Chapter 3 1

NCERT Solutions for Class 11 Maths Chapter 3 Trigonometric Functions

NCERT solutions Class 11 Maths Chapter 3 Trigonometric Functions are extremely beneficial in developing mathematical reasoning in students. With the help of these well-structured resources, students will gain a simplistic approach for efficient exam preparation. The carefully placed illustrations, questions, and examples present in these solutions are sufficient to enhance the fundamental math knowledge to excel in exams. Kids can easily plan their curriculum and revision format with the help of these solutions. To practice the exercise-wise NCERT Solutions Class 11 Maths Trigonometric Functions, try the links given below.

Class 11 Maths Chapter 3 Ex 3.1 - 7 Questions
Class 11 Maths Chapter 3 Ex 3.2 - 10 Questions
Class 11 Maths Chapter 3 Ex 3.3 - 25 Questions
Class 11 Maths Chapter 3 Ex 3.4 - 9 Questions
Class 11 Maths Chapter 3 Miscellaneous Ex - 10 Questions

☛ Download Class 11 Maths Chapter 3 NCERT Book

Topics Covered: NCERT solutions Class 11 Maths Chapter 3 Trigonometric Functions cover some important topics, including an introduction to trigonometric ratios and identities, the measure of angles, signs, domain and range of trigonometric functions . The other important topic included in these solutions is the trigonometric solutions of the sum and difference of two angles using formulas .

Total Questions: Class 11 Maths Chapter 3 Trigonometric Functions has 51 questions in 4 exercises plus 10 questions in one miscellaneous exercise. These are primarily based on the representation of trigonometric functions, their applications, and formulas.

List of Formulas in NCERT Solutions Class 11 Maths Chapter 3

Memorizing important formulas and concepts is necessary to understand the terms and operations related to trigonometric functions clearly. NCERT Solutions Class 11 Maths Chapter 3 will provide detailed knowledge of all these along with their applications through interesting illustrations. Each concept in these solutions is well-explained with suitable examples and sample problems to promote an in-depth understanding of this topic. Formulas form an integral part of this lesson hence, creating a formulas sheet can be useful for students when they need to practice this topic. Some of the important terms, formulas, and concepts related to Trigonometric Functions explained in these solutions are listed below:

Trigonometric Functions: Trigonometric Functions are real functions that relate the angle of a r ight-angled triangle to the ratio of the length of its sides. Sin, Cos, and Tan are the three primary functions.
Trigonometric Equations: Trigonometric equations are equations that involve the use of trigonometric functions. These trigonometric equations are also known as trigonometric identities when the values of unknown angles for which the functions are defined are satisfied.
Trigonometric Identities: A trigonometric equation that involves the sum and difference of angles represent a trigonometric identity. For example, sin 2 θ + cos 2 θ = 1
Sum and Difference Identities: The sum and difference identities include the following formulas.
sin(x+y) = sin(x)cos(y) + cos(x)sin(y)
cos(x+y) = cos(x)cos(y) – sin(x)sin(y)
tan(x+y) = (tan x + tan y)/ (1−tan x • tan y)
sin(x–y) = sin(x)cos(y) – cos(x)sin(y)
cos(x–y) = cos(x)cos(y) + sin(x)sin(y)
tan(x−y) = (tan x–tan y)/ (1+tan x • tan y)

FAQs on NCERT Solutions Class 11 Maths Chapter 3

What is the importance of ncert solutions for class 11 maths chapter 3 trigonometric functions.

NCERT Solutions for Class 11 Maths Chapter 3 Trigonometric Functions are designed by well-qualified teachers and math experts to promote proficient math learning. Each exercise of these solutions is formulated as per the CBSE guidelines to support in-depth learning of Trigonometric Functions and their relations. These competently structured solutions are suitable to enhance math proficiency in students. Regular practice of these solutions will boost students’ confidence in scoring well.

What are the Important Topics Covered in NCERT Solutions Class 11 Maths Chapter 3?

NCERT Solutions Class 11 Maths Chapter 3 briefly introduces trigonometric ratios and identities along with some core concepts previously studied in grade 10. The important topics covered in these solutions are angle measures, trigonometric functions, their signs, domain, and range. The sum and difference of two angles using trigonometric functions are also included in this chapter.

Do I Need to Practice all Questions Provided in Class 11 Maths NCERT Solutions Trigonometric Functions?

NCERT Solutions Class 11 Maths Trigonometric Functions are designed in an effective way to facilitate the in-depth learning of concepts. Every question included in these solutions is aimed to improve the conceptual clarity for students to master them easily. The fundamental knowledge of Trigonometric Functions and their use will allow students to apply their knowledge in practical situations. These solutions also form the basis for studying advanced math topics, including calculus. Thus, all sums must be practiced with laser focus.

How Many Questions are there in Class 11 Maths NCERT Solutions Chapter 3 Trigonometric Functions?

NCERT Solutions for Class 11 Maths Chapter 3 Trigonometric Functions has 61 questions in 5 exercises. These problems are sufficient to provide a deep-seated understanding of the entire topic of trigonometric functions, including important formulas, identities, ratios, and operations related to Trigonometric Functions. The jargon-free and lucid math vocabulary used in these solutions are quite proficient in easily imparting a clear step-by-step understanding of each topic as well as subtopics.

What are the Important Formulas in Class 11 Maths NCERT Solutions Chapter 3?

NCERT Solutions Class 11 Maths Chapter 3 explains the formulas related to the sum and difference of two angles in trigonometric functions. Some of the important concepts related to this topic are based on deriving expressions for trigonometric identities of the sum and difference of angles. These vital concepts are described comprehensively with the help of interesting examples for students to grasp them better. Additionally, kids need to also revise the formulas they have encountered in previous classes as those are also necessary to attempt class 11 trigonometry problems.

Why Should I Practice NCERT Solutions for Class 11 Maths Chapter 3 Trigonometric Functions?

NCERT Solutions for Class 11 Maths Chapter 3 Trigonometric Functions is a reliable source of learning that gives full guidance for excellent exam preparation. With the help of these solutions, students can cover the whole syllabus of CBSE Class 11 Maths Chapter 3. The format of these solutions is quite intuitive to promote simple and easy learning. Thus, to get the best results kids need to practice these solutions.

Important Questions for Class 11 Maths Chapter 3 Trigonometric Functions - PDF Download

trigonometry case study questions class 11

CBSE class 11 maths chapter 3 Trigonometric Functions important questions are prepared for the students who are preparing for class 11 maths exams. Trigonometric functions class 11th maths important questions have been developed by subject experts of eSaral for enhancing the problem-solving ability to score good marks in exams. You can go through the trigonometry questions for class 11 which are based on the updated syllabus of CBSE. These important questions are solved in a step by step method which helps you to understand the concepts easily.

Class 11 maths chapter 3 Trigonometric Functions is one of the easiest chapters which includes questions based on different formulas. To solve trigonometric questions for class 11, you have to learn and remember all the essential formulas of trigonometric functions. Each and every concept of trigonometric functions has been covered in important questions of class 11 mathematics chapter 3 curated by eSaral that will help you to achieve great marks in final exams.

Students can refer to trigonometry questions with answers pdf provided by experts of mathematics. In class 11th trigonometry important questions, all the concepts are explained in precise language. This will give you a quick understanding of all the concepts and formulas while solving these important questions. Our expert teachers of mathematics at eSaral have also provided important questions of trigonometry class 11 in free PDF format which you can download from the official website of eSaral and practice these questions even before the main exam.

Important Topics & Sub-topics of Trigonometric Functions Class 11 Maths

Chapter 3 Trigonometric Functions deals with the relation between angles and sides of triangles. This chapter is essential and a scoring one for the students of class 11. Thus, it is vital for students to have a thorough understanding of all the significant topics and sub-topics of trigonometric functions. In class 11 maths chapter 3, you will delve into the difficulties of trigonometric functions and concepts based on them. Our subject experts of eSaral have combined all the topics and sub-topics of trigonometric functions in the tabulated structure mentioned below.

Class 11 Maths Chapter 3 Trigonometric Functions Weightage

CBSE class 11 maths chapter 3 Trigonometric Functions forms solid foundations for advance level concepts of mathematical studies. In chapter 3, understanding the weightage of significant topics helps you to prioritize your preparations in an effective way. This chapter carries the highest marks in unit one. Thus, students should be thorough with the concepts of trigonometric functions chapter 3 class 11 maths to score desired marks in examination.

The weightage and marks distribution can vary from one education board to another one so students are advised to check the official website of CBSE to get the correct information regarding weightage of chapter 3. Chapter 3 Trigonometric Functions has topics angles, domain and range of trigonometric functions, and trigonometric functions of sum and difference of two angles which you must be well-versed to solve questions effectively and easily in exam. In order to score full marks in trigonometric functions, practice important questions of trigonometry class 11 maths provided on eSaral. You can also solve examples and questions mentioned in exercises of chapter 3 to grasp the knowledge of essential topics of trigonometric functions.

Tips to Solve Class 11 Maths Chapter 3 Trigonometric Functions

Class 11 maths chapter 3 Trigonometric Functions is an easy chapter where you can score full marks by deeply analyzing and comprehending the main concepts of trigonometry. By solving 11th class trigonometry important questions, you will get to know some tips and tricks that help you to solve the questions quickly. Check out some useful tips provided below by eSaral’s subject experts of mathematics.

Firstly, Students should never miss the formulas of trigonometric functions as these formulas are crucial to solve the questions correctly.

To understand the concepts of trigonometry deeply, you should use the resources like trigonometry important questions for class 11 available on eSaral.

Trigonometric formulas are an essential part of chapter 3. Thus, forming a formula chart can be a helpful tool for students whenever they need to practice trigonometry based questions.

There are some significant topics such as domain and range of trigonometric functions, relation between degree and radian, degree measure of angles etc. which students need to understand to solve questions without any error.

Benefits of Solving Class 11 Maths Chapter 3 Important Questions with Answers

Downloading and practicing important questions class 11 maths chapter 3 will give you an in-depth understanding of trigonometric functions. Students must solve trigonometry problems for class 11 by eSaral for better preparation of exams. Here, our subject experts of mathematics have provided numerous benefits of solving class 11 maths chapter 3 important questions which can be checked below.

Conceptual Understanding - By practicing class 11 maths important questions solidify the fundamental concepts of trigonometric functions. All the important questions of trigonometric functions class 11th have deeply included each question which describes the core principles of trigonometry. This process helps you to revise the concepts which you have studied in theoretical knowledge acquired in the classroom.

Preparing for Examination - Class 11 maths chapter 3 important questions not only help you to reinforce the theoretical knowledge of trigonometric functions but also familiarize you with question format and type of questions asked in board exams.

Boost Confidence - Solving class 11 maths chapter 3 important questions help students to recall all the vital concepts of trigonometry. You also get to learn the easy methods of solving trigonometric functions that boost your self-confidence.

Improve Time Management - By frequently practicing important questions of trigonometry class 11 maths chapter 3, You will be able to solve questions within the time allotted for question paper in the main exam. This will help you to improve your time management skills.

Frequently Asked Questions

Answer 1. To solve trigonometry based questions, students must memorize all the formulas of trigonometric functions which help you to solve any question asked in examinations related to trigonometric functions. You should also practice questions of exercises mentioned in chapter 3. This provides deep comprehension of concepts of trigonometric functions.

Answer 2. There are a total of 3 exercises as well as one miscellaneous exercise which must be solved to score good marks in the final exam.

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NCERT Solutions for Class 11 Maths Chapter 3 – Trigonometric Functions

Ncert solutions for class 11 maths chapter 3 – trigonometric functions pdf.

Free PDF of NCERT Solutions for Class 11 Maths Chapter 3 – Trigonometric Functions includes all the questions provided in NCERT Books prepared by Mathematics expert teachers as per CBSE NCERT guidelines from Mathongo.com. To download our free pdf of Chapter 3 – Trigonometric Functions Maths NCERT Solutions for Class 11 to help you to score more marks in your board exams and as well as competitive exams.

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Syllabus for the Session 2023-24

CBSE Syllabus

Case Study Questions

Case Study on Sets CS-2 CS-3 CS-4 CS-5

Case Study on Relations & Functions CS-2 CS-3

Case Study on Trigonometric Functions

Case Study on Complex Numbers

Case Study on Linear Inequalities

Case Study on Permutations and Combinations

Case Study on Sequences & Series

Case Study on Straight Lines

Case Study on Conic Sections

Case Study on Statistics

Case Study on Probability

Pdf of Case Studies

MCQs for Practice

Chapter 1 - Sets

Chapter 2 - Relations & Functions

Chapter 3 - Trigonometric Functions

Chapter 4 - Complex Numbers & Quadratic Equations

Chapter 5 - Linear Inequalities

Chapter 6 - Permutations & Combinations

Chapter 7 - Binomial Theorem

Chapter 8 - Sequences & Series

Chapter 9 - Straight Line

Chapter 1 0 - Conic Sections

Chapter 1 1 - Introduction to Three-dimensional Geometry

Chapter 12 - Limits & D erivatives

Chapter 13 - Statistics

Chapter 14 - Probability

Answers of MCQs

Assertion & Reasoning Questions

Relations & Functions

Trigonometric Functions

Complex Numbers

Linear Inequalities

Permutations & Combinations

Binomial Theorem

Sequences & Series

Straight Lines

Conic Sections

Introduction to Three-Dimensional Geometry

Limits & derivatives

Probability

Topic Wise Assignments of Previous Year Questions

Relations and Functions

Straight Line

Limits & Derivatives

Question Papers - DoE, Delhi

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SA2(QP) SA2(MS) COMP(QP) COMP(MS)

Session 201 6 -20 17

SA1(QP) SA2(QP) SA2(MS) COMP(QP) COMP(MS)

Session 201 7 -201 8

SA2(QP) SA2(MS) COMP(QP) COMP(MS)

Session 201 8 -201 9

SA2(QP) SA2(MS) COMP(QP) COMP(MS)

Session 201 9 -20 20

SA2(QP) SA2(MS)

Session 2020-21

Video Explanation: Part A Part B Section III Part B Section IV Part B Section V

Session 2021-22

Question Paper

Video Explanation: Section A Section B Section C

Session 2022-23

Sample Question Paper for Mid-Term Exam