NCERT Solutions for Class 11 Mathematics Chapter 3 Trigonometric Functions
NCERT solutions for Class 11 Mathematics Chapter 3 Trigonometric Functions – complete answers & explanations
This chapter of Class 11 Mathematics focuses on trigonometric functions, which are an important part of higher-level maths and many real-life applications. Students learn about angles, radian measure, and how trigonometric functions behave. Understanding this chapter helps build a strong base for calculus, physics, and advanced problem-solving. These NCERT solutions provide clear and reliable answers that help students practice effectively and gain confidence. Download the worksheet and practice alongside solutions for better clarity. With the right guidance and consistent practice, mastering trigonometric functions becomes easier. Book a free trial now to get expert guidance and strengthen your concepts step by step.
What this NCERT chapter covers?
1. Introduction to trigonometry and its
real-life applications in science and engineering.
2. Understanding angles, their measurement, and direction (positive and negative angles).
3. Learning degree and radian measures and converting between them.
4. Relationship between real numbers and radian measures.
5. Concepts of unit circle and trigonometric functions like sin, cos, tan.
6. Understanding quadrantal angles and their values.
7. Important identities such as sin²x + cos²x = 1.
8. Signs of trigonometric functions in different quadrants.
9. Domain and range of trigonometric functions.
10. Behaviour and graphs of trigonometric functions.
11. Solving problems using trigonometric identities.
12. Application of trigonometric functions in various mathematical problems.
How to use these NCERT solutions?
1. First attempt all questions from
the worksheet on your own without looking at the answers.
2. After completing, compare your answers with the given solutions carefully.
3. Focus on understanding where mistakes happen instead of just correcting them.
4. Practice similar types of questions multiple times to improve accuracy.
5. Follow the order of questions exactly as given to maintain proper learning flow.
6. Use these solutions to revise important formulas and concepts regularly.
7. Parents and teachers can guide students by discussing each solution step-by-step.
8. For difficult questions, try solving again after reviewing the solution.
9. Ensure proper understanding of concepts rather than memorising answers.
10. Use the solutions as a tool to build confidence before exams.
Important tips & tricks for students
1. Always remember key formulas and identities for quick problem solving.
2. Practice conversions between degree and radian regularly.
3. Pay attention to the signs of trigonometric functions in different quadrants.
4. Avoid calculation mistakes by writing steps clearly.
5. Revise unit circle values frequently.
6. Focus on understanding concepts instead of rote learning.
7. Solve previous questions to improve speed and accuracy.
8. Double-check answers especially in trigonometric identities.
9. Practice more numerical problems for better clarity.
10. Stay consistent with revision to score full marks.
NCERT solutions – complete answer key
EXERCISE 3.1
(i) 5π/36
(ii) –19π/72
(iii) 4π/3
(iv) 26π/9
(i) 123°45′
(ii) –229°5′ (approx)
(iii) 300°
(iv) 210°
12π 12.6°
20π/3 cm
1 2
3 4
5
5 : 4
(i) 2/15 radian
(ii) 1/5 radian
(iii) 7/25 radian
6
7
EXERCISE 3.2
sin x = –√3/2
tan x = √3
cosec x = –2√3/3
sec x = –2
cot x = 1/√3
1 cos x = –4/5
tan x = –3/4
cosec x = 5/3
sec x = –5/4
cot x = –4/3
2
sin x = –3/5
cos x = –4/5
tan x = 3/4
cosec x = –5/3
sec x = –5/4
√3/2
cos x = 5/13
sin x = –12/13
tan x = –12/5
cosec x = –13/12
cot x = –5/12
–2 √3/2
sin x = 5/13
cos x = –12/13
cosec x = 13/5
sec x = –13/12
cot x = –12/5
–√3
3
4
5
6 7
8 9
10
–1
EXERCISE 3.3
1
(1 + tan x)/(1 – tan x)
tan x/4
cot (3x/2)
1
(i) (√6 + √2)/4
(ii) 2 – √3
sin 4x sin 8x
–2 sin x
1 2
3 4
5 6
7 8
9 10
2
6 10
sin (x + y)
cot x
cos x
sin 2x sin 10x
4 cos²x sin 4x
cot x (sin 5x – sin 3x) –2 tan x
tan [(x – y)/2]
tan (3x/2) sin x
1
11 12
13
15 16
17
18
14
19 20
21 22
tan 4x 1 – 8 sin²x cos²x
32 cos⁶x – 48 cos⁴x + 18 cos²x – 1 25
23 24
Why NCERT solutions help students?
NCERT solutions help students build strong conceptual understanding and improve exam readiness. They provide the correct approach to answering questions and ensure clarity in problem-solving methods. Practising these solutions regularly boosts confidence and helps students perform better in exams.
Help your child build strong Mathematics fundamentals with expert-guided learning support.
Book a free trial!