NCERT Solutions for Class 11 Maths Chapter 3 Trigonometric Functions

Infinity Learn offers NCERT Solutions for Class 11 Maths Chapter 3 - Trigonometric Functions, carefully prepared by experienced educators. These solutions follow the latest CBSE Syllabus 2025-26 and are designed according to updated board guidelines. The solutions are presented step-by-step, catering to different levels of student understanding and considering the exam's marking scheme.

Chapter 3: Trigonometric Functions holds great importance in Class 11 Mathematics. Although the chapter includes various formulas and mathematical concepts, Infinity Learn simplifies these topics using easy-to-understand explanations and smart learning tricks, helping students grasp and retain the concepts effectively.

Trigonometry, a branch of mathematics developed to address problems involving triangles, has widespread applications — from measuring ocean tides to designing complex electronic circuits. Students are introduced to basic trigonometric identities and ratios in earlier classes. In Class 11, these concepts are expanded into trigonometric functions and their properties.

NCERT Solutions for Class 11 Maths Chapter 3 Trigonometric Functions

The NCERT Solutions provided by Infinity Learn help students strengthen their conceptual understanding, improve problem-solving skills, and maximize their scores in exams by offering clear explanations and well-structured solutions for every topic covered in the chapter.

NCERT Solutions for Class 11 Maths Chapter 3 Trigonometric Functions - Download PDF

NCERT Solutions for Class 11 Maths Chapter 3 Trigonometric Functions download PDF from IL.

NCERT Solutions for Class 11 Maths Chapter 3 Trigonometric Functions - Question and Answer

Basic Conceptual Questions

1. What is the principal value of sin⁻¹(1/2)?
   Answer: π/6
2. Define periodic function.
   Answer: A function f(x) is periodic if there exists a positive number T such that f(x + T) = f(x) for all x.
3. Write the value of sin(0).
   Answer: 0
4. What is the value of cos(π)?
   Answer: -1
5. What is the period of sin(x)?
   Answer: 2π
6. Find tan(π/4).
   Answer: 1
7. Write the domain and range of sin(x).
   Answer: Domain: (-∞, ∞), Range: [-1, 1]
8. What is the value of sec(0)?
   Answer: 1
9. State the range of cot(x).
   Answer: (-∞, ∞)
10. State the period of tan(x).
    Answer: π

Trigonometric Identities & Properties

11. State the identity involving sin²x and cos²x.
    Answer: sin²x + cos²x = 1
12. Express tan(x) in terms of sin(x) and cos(x).
    Answer: tan(x) = sin(x)/cos(x)
13. State the cofunction identity of sin(x).
    Answer: sin(π/2 - x) = cos(x)
14. What is the value of sin²x + cos²x + tan²x?
    Answer: sin²x + cos²x + tan²x = 1 + tan²x
15. Write the formula for cos(2x).
    Answer: cos(2x) = 2cos²x - 1 or cos²x - sin²x
16. Simplify sin(π - x).
    Answer: sin(π - x) = sin(x)
17. Simplify cos(π - x).
    Answer: cos(π - x) = -cos(x)
18. Simplify tan(π - x).
    Answer: tan(π - x) = -tan(x)

Conversion & Angle Measurement

19. Convert 60° into radians.
    Answer: π/3 radians
20. Convert π/6 radians into degrees.
    Answer: 30°
21. Convert -π/4 radians into degrees.
    Answer: -45°
22. Express 270° in radians.
    Answer: 3π/2 radians
23. Express 7π/6 radians in degrees.
    Answer: 210°

Application-Based Questions

24. Find the value of sin(225°).
    Answer: -√2/2
25. Find the exact value of cos(150°).
    Answer: -√3/2
26. Find tan(330°).
    Answer: -1/√3
27. If sinθ = 3/5, find cosθ (θ in 1st quadrant).
    Answer: cosθ = 4/5
28. If cosθ = 12/13, find sinθ (θ in 1st quadrant).
    Answer: sinθ = 5/13
29. If tanA = 3/4, find sinA and cosA.
    Answer: sinA = 3/5, cosA = 4/5

Higher Order and Formula-Based Questions

30. Find the general solution of sinx = 1/2.
    Answer: x = nπ + (-1)ⁿ(π/6), where n ∈ Z
31. Find the general solution of cosx = √3/2.
    Answer: x = 2nπ ± π/6, where n ∈ Z
32. Find the general solution of tanx = 1.
    Answer: x = nπ + π/4, where n ∈ Z
33. Write the formula of sin(A ± B).
    Answer: sin(A ± B) = sinAcosB ± cosAsinB
34. Write the formula of cos(A ± B).
    Answer: cos(A ± B) = cosAcosB ∓ sinAsinB
35. Find the value of sin(75°) using compound angle formula.
    Answer: (√6 + √2)/4
36. Find the value of cos(15°) using compound angle formula.
    Answer: (√6 + √2)/4
37. Find sin²θ - cos²θ if θ = π/4.
    Answer: 0
38. If sin(A) = 3/5 and A is acute, find cos(2A).
    Answer: 7/25
39. Prove: tan(A) + cot(A) = (sin²A + cos²A) / (sinA cosA).
    Answer: Proved using identity sin²A + cos²A = 1
40. Prove: 1 + tan²A = sec²A.
    Answer: Standard trigonometric identity.