NCERT Solutions for Class 11 Maths Chapter 3 Trigonometric Functions

This worksheet provides complete and accurate NCERT Solutions for Class 11 Mathematics Chapter Trigonometric Functions. This chapter introduces students to the concept of angles, measurement in radians and degrees, and the fundamental trigonometric functions. It is an important chapter as it builds the foundation for higher mathematics, including calculus and advanced algebra. This worksheet helps students understand and practice all concepts with precise NCERT-based answers, ensuring clarity and confidence.

Chapter summary: stories, poems & themes

This chapter is concept-based and does not include stories or poems. It focuses on mathematical understanding of trigonometric functions, angle measurement, and identities. Students learn through numerical problems and concept application. The worksheet is fully activity-based in terms of calculations and problem-solving, helping students build strong analytical skills.

What this NCERT chapter covers?

• Understanding of angle measurement in radians and degrees 
• Conversion between degree and radian measures 
• Evaluation of trigonometric functions 
• Understanding relationships between trigonometric ratios 
• Application of trigonometric identities 
• Problem-solving using trigonometric expressions 

How to use these NCERT solutions?

Students should first attempt all questions on their own to test their understanding. After attempting, they can refer to these NCERT solutions to verify answers and correct mistakes. Parents and teachers can use this worksheet to guide students and track their progress. The solutions follow the exact NCERT order and structure, making it easy for revision and systematic learning.

Student tips & learning tricks

• Always remember key trigonometric values for standard angles 
• Be careful with signs of trigonometric functions in different quadrants 
• Practice conversions between degrees and radians regularly 
• Double-check calculations involving fractions and square roots 
• Follow step-by-step solving methods as per NCERT 

Why NCERT solutions are important?

NCERT Solutions help students build a strong conceptual foundation. They ensure that students learn correct methods and avoid common mistakes. These solutions improve problem-solving skills, boost confidence, and prepare students for school exams and competitive tests. Regular practice with NCERT-based solutions ensures better understanding and long-term retention.

Complete answer key – NCERT solutions

Exercise 3.1

1 
(i) 5π/36 
(ii) –19π/72 
(iii) 4π/3 
(iv) 26π/9 

2 
(i) 123°45′ 
(ii) –229°5′ (approx) 
(iii) 300° 
(iv) 210° 

3 
12π 
12.6° 

4 
20π/3 cm 

5 
1 
2 
3 
4 
5 

6 
5 : 4 

7 
(i) 2/15 radian 
(ii) 1/5 radian 
(iii) 7/25 radian 

Exercise 3.2

1 
sin x = –√3/2 
tan x = √3 
cosec x = –2√3/3 
sec x = –2 
cot x = 1/√3 

2 
cos x = –4/5 
tan x = –3/4 
cosec x = 5/3 
sec x = –5/4 
cot x = –4/3 

3 
sin x = –3/5 
cos x = –4/5 
tan x = 3/4 
cosec x = –5/3 
sec x = –5/4 

4 
√3/2 

5 
cos x = 5/13 
sin x = –12/13 
tan x = –12/5 
cosec x = –13/12 
cot x = –5/12 

6 
–2 

7 
√3/2 

8 
sin x = 5/13 
cos x = –12/13 
cosec x = 13/5 
sec x = –13/12 
cot x = –12/5 

9 
–√3 

10 
–1 

Exercise 3.3

1 
(1 + tan x)/(1 – tan x) 

2 
tan x/4 

3 
cot (3x/2) 

4 
1 

5 
(i) (√6 + √2)/4 
(ii) 2 – √3 

6 
sin 4x 
sin 8x 

7 
–2 sin x 

8 
1 

9 
2 

10 
6 

11 
10 

12 
sin (x + y) 

13 
cot x 

14 
cos x 

15 
sin 2x 
sin 10x 

16 
4 cos²x sin 4x 

17 
cot x (sin 5x – sin 3x) 

18 
–2 tan x 

19 
tan [(x – y)/2] 

20 
tan (3x/2) 

21 
sin x 

22 
tan 4x 

23 
1 – 8 sin²x cos²x 

24 
32 cos⁶x – 48 cos⁴x + 18 cos²x – 1 

25 
1 

Master trigonometric concepts easily with accurate NCERT Solutions designed for Class 11 Mathematics success.
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