Important Questions for Class 11 Maths Chapter 3 Trigonometric Functions
Important Questions for Class 11 Maths Chapter 3 has been provided here. Students can refer to these questions before their examinations for better preparation.
Ananya Gupta12 Nov, 2024
Share
Important Questions for Class 11 Maths Chapter 3: Important Questions for Class 11 Maths Chapter 3 Trigonometric Functions are created to help students grasp the core concepts of trigonometry which is important for advanced mathematical problem-solving.
Solving these questions helps students build a strong foundation in trigonometry, making it easier to tackle more complex questions in exams and other mathematical applications. By working through these problems, students can reinforce their knowledge enhance their problem-solving skills and gain confidence in approaching this critical chapter.Important Questions for Class 11 Maths Chapter 3 Overview
Important Questions for Class 11 Maths Chapter 3 Trigonometric Functions have been created by subject experts at Physics Wallah to provide students with a deep understanding of trigonometry’s fundamental concepts. Each question has been chosen to align with the curriculum, helping students practice problem-solving techniques and understand how to approach different types of trigonometric problems effectively. Practicing these expert-prepared questions enables students to strengthen their foundational knowledge and boost their confidence for exams.Important Questions for Class 11 Maths Chapter 3 PDF
Important Questions for Class 11 Maths Chapter 3 Trigonometric Functions PDF is available below for download. By using this PDF students can easily access the most relevant questions for practice and exam preparation, helping them enhance their understanding of trigonometry and improve problem-solving skills. Download the PDF to get started with your preparation.Important Questions for Class 11 Maths Chapter 3 PDF
Important Questions For Class 11 Maths Chapter 3 Trigonometric Functions
Here is the Important Questions For Class 11 Maths Chapter 3 Trigonometric Functions-Q. No.1: In any triangle ABC, prove that a sin (B – C) + b sin (C – A) + c sin (A – B) = 0.
Solution:
In any triangle ABC, a/sin A = b/sin B = c/sin C = k a = k sin A, b = k sin B, c = k sin C LHS = a sin (B – C) + b sin (C – A) + c sin (A – B) = k sin A [sin B cos C – cos B sin C] + k sin B [sin C cos A – cos C sin A] + k sin C [sin A cos B – cos A sin B] = k sin A sin B cos C – k sin A cos B sin C + k sin B sin C cos A – k sin B cos C sin A + k sin C sin A cos B – k sin C cos A sin B = 0 = RHS Hence proved that a sin (B – C) + b sin (C – A) + c sin (A – B) = 0.Q.No.2: Find the radius of the circle in which a central angle of 60° intercepts an arc of length 37.4 cm (use π = 22/7).
Solution:
Given, Length of the arc = l = 37.4 cm Central angle = θ = 60° = 60π/180 radian = π/3 radians We know that, r = l/θ = (37.4) * (π / 3) = (37.4) / [22 / 7 * 3] = 35.7 cm Hence, the radius of the circle is 35.7 cm.Q. No.3: A wheel makes 360 revolutions in one minute. Through how many radians does it turn in one second?
Solution:
Given, Number of revolutions made by the wheel in 1 minute = 360 1 minute = 60 seconds Number of revolutions in 1 second = 360/60 = 6 Angle made in 1 revolution = 360° Angles made in 6 revolutions = 6 × 360° Radian measure of the angle in 6 revolutions = 6 × 360 × π/180 = 6 × 2 × π = 12π Hence, the wheel turns 12π radians in one second.Q. No. 4: Find the value of √3 cosec 20° – sec 20°.
Solution:
√3 cosec 20° – sec 20°
Q. No. 5: Show that tan 3x tan 2x tan x = tan 3x – tan 2x – tan x.
Solution:
Let 3x = 2x + x Taking “tan” on both sides, tan 3x = tan (2x + x) We know that,
tan 3x = (tan 2x + tan x)/ (1- tan 2x tan x)
tan 3x(1 – tan 2x tan x) = tan 2x + tan x
tan 3x – tan 3x tan 2x tan x = tan 2x + tan x
tan 3x – (tan 2x + tan x) = tan 3x tan 2x tan x
Therefore, tan 3x – tan 2x – tan x = tan 3x tan 2x tan x.
Q. No. 6: Prove that:
Solution:
LHS
= RHS
Hence proved.
Q. No. 7: Find the value of cos 570° sin 510° + sin (-330°) cos (-390°).
Solution:
LHS =cos (570)sin (510) + sin (- 330)cos (- 390) = cos (570) sin (510) + [ – sin (330) ]cos (390) [ because sin( – x ) = – sin x and cos( – x ) = cos x ] = cos (570)sin(510) – sin (330) = cos (90 * 6 + 30) sin (90 * 5 + 60) – sin (90 * 3 + 60) cos (90 * 4 + 30) = – cos (30) cos (60) – [ – cos (60) ] cos (30) = – cos (30) cos (60) + cos (30) sin (60) = 0Q. No. 8: Find the general solution of the following equation.
Solution:
Given,
cos
2
θ + 3 sin θ + 3 sin
2
θ = 0
1 – sin
2
θ + 3 sin θ + 3 sin
2
θ = 0
2 sin
2
θ + 3 sin θ + 1 = 0
2sin
2
θ + 2 sin θ + sin θ + 1 = 0
2 sin θ (sin θ +1 ) + 1 (sin θ + 1) = 0
(2 sin θ + 1) (sin θ + 1) = 0
2 sin θ + 1 = 0, sin θ + 1 = 0
sin θ = -½, sin θ = -1
θ = nπ – (-1)
n
π/6, θ = nπ – (-1)
n
π/2; n ∈ Z
Q. No. 9: Show that 2 sin 2 β + 4 cos (α + β) sin α sin β + cos 2 (α + β) = cos 2α.
Solution:
LHS = 2 sin 2 β + 4 cos (α + β) sin α sin β + cos 2(α + β) = 2 sin 2 β + 4 (cos α cos β – sin α sin β) sin α sin β + (cos 2α cos 2β – sin 2α sin 2β) = 2 sin 2 β + 4 sin α cos α sin β cos β – 4 sin 2 α sin 2 β + cos 2α cos 2β – sin 2α sin 2β = 2 sin 2 β + sin 2α sin 2β – 4 sin 2 α sin 2 β + cos 2α cos 2β – sin 2α sin 2β = (1 – cos 2β) – (2 sin 2 α) (2 sin 2 β) + cos 2α cos 2β = (1 – cos 2β) – (1 – cos 2α) (1 – cos 2β) + cos 2α cos 2β = cos 2α = RHS Therefore, 2 sin 2 β + 4 cos (α + β) sin α sin β + cos 2 (α + β) = cos 2αQ. No. 10: Prove that:
Solution:
LHS=(sec 8θ -1 )/ (sec4θ -1) =(1/(cos8θ) -1 )/ (1/(cos4θ) -1) =((1-cos8θ)cos4θ )/ ((1-cos4θ) cos8θ) =(2sin 2 4θcos4θ )/ ((2sin 2 2θ) cos8θ) =(2sin4θcos4θsin4θ )/ ((2sin 2 2θ) cos8θ) =(sin8θ * 2sin2θcos2θ )/ ((2sin 2 2θ) cos8θ) =(tan8θ * cos2θ )/ (sin2θ) = (tan8θ) /(tan 2θ) = RHS Hence proved.Benefits of Solving Important Questions For Class 11 Maths Chapter 3 Trigonometric Functions
Solving Important Questions for Class 11 Maths Chapter 3 Trigonometric Functions provide several key benefits: Improved Conceptual Understanding : These questions cover a variety of topics, allowing students to reinforce their understanding of trigonometric functions, identities and equations. Exam Readiness : Practicing these questions helps familiarize students with the types of problems they may encounter in exams, ensuring they are well-prepared for any question format. Enhanced Problem-Solving Skills : By tackling diverse problems students develop strong problem-solving abilities which are important for tackling complex mathematical challenges. Time Management : Regular practice helps students manage time effectively during exams, as they become adept at solving problems more quickly and efficiently. Confidence Boost : Solving a wide range of questions from the chapter increases confidence in tackling various trigonometric problems, making students more confident when facing their exams. Better Retention : Frequent practice improves retention and recall of important formulas and concepts which is important for mastering trigonometry.Important Questions for Class 11 Maths Chapter 3 FAQs
What are trigonometric functions?
Trigonometric functions are mathematical functions that relate the angles of a triangle to the ratios of its sides. The primary trigonometric functions are sine (sin), cosine (cos), tangent (tan), secant (sec), cosecant (csc) and cotangent (cot).
What is the unit circle in trigonometry?
The unit circle is a circle with a radius of 1 centered at the origin of a coordinate plane. The angles in the unit circle correspond to the values of the trigonometric functions, helping students visualize and understand how the functions behave.
What is the significance of trigonometric functions in solving triangles?
Trigonometric functions are crucial in solving right-angled triangles. They help in finding unknown sides or angles of a triangle when given some information about the sides or angles.
How can I simplify trigonometric expressions?
To simplify trigonometric expressions, use identities like the Pythagorean identities, reciprocal identities, and sum or difference identities.
Talk to a counsellorHave doubts? Our support team will be happy to assist you!
Check out these Related Articles
Join 15 Million students on the app today!
Live & recorded classes available at easeDashboard for progress trackingMillions of practice questions at your fingertips
Free Learning Resources
PW Books
Notes (Class 10-12)
PW Study Materials
Notes (Class 6-9)
Ncert Solutions
Govt Exams
Class 6th to 12th Online Courses
Govt Job Exams Courses
UPSC Coaching
Defence Exam Coaching
Gate Exam Coaching
Other Exams
Know about Physics Wallah
Physics Wallah is an Indian edtech platform that provides accessible & comprehensive learning experiences to students from Class 6th to postgraduate level. We also provide extensive NCERT solutions, sample paper, NEET, JEE Mains, BITSAT previous year papers & more such resources to students. Physics Wallah also caters to over 3.5 million registered students and over 78 lakh+ Youtube subscribers with 4.8 rating on its app.
We Stand Out because
We provide students with intensive courses with India’s qualified & experienced faculties & mentors. PW strives to make the learning experience comprehensive and accessible for students of all sections of society. We believe in empowering every single student who couldn't dream of a good career in engineering and medical field earlier.
Our Key Focus Areas
Physics Wallah's main focus is to make the learning experience as economical as possible for all students. With our affordable courses like Lakshya, Udaan and Arjuna and many others, we have been able to provide a platform for lakhs of aspirants. From providing Chemistry, Maths, Physics formula to giving e-books of eminent authors like RD Sharma, RS Aggarwal and Lakhmir Singh, PW focuses on every single student's need for preparation.
What Makes Us Different
Physics Wallah strives to develop a comprehensive pedagogical structure for students, where they get a state-of-the-art learning experience with study material and resources. Apart from catering students preparing for JEE Mains and NEET, PW also provides study material for each state board like Uttar Pradesh, Bihar, and others
Copyright © 2025 Physicswallah Limited All rights reserved.