📐 CBSE · Class 11 · Mathematics · Chapter 3

Trigonometric
Functions

Complete chapter resources for CBSE Class 11 Mathematics — topic breakdown, key identities and formulas, sample questions, previous year board questions, and instant AI question paper generation.

5Topics
8–10Board marks
8Sample questions
3PYQ included
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Key Formulas — Chapter 3
  • Pythagorean: sin²x + cos²x = 1
  • Compound angle: sin(A+B) = sinA cosB + cosA sinB
  • Double angle: sin 2A = 2 sinA cosA
  • cos 2A: cos²A − sin²A = 2cos²A − 1
  • General soln (sin): x = nπ + (−1)ⁿα, n ∈ Z
  • Conversion: π rad = 180°
Chapter Overview

What this chapter covers

Chapter 3 of NCERT Class 11 Mathematics extends the trigonometry studied in Classes 9 and 10 from the restricted domain of right-angled triangles to all real numbers. The chapter begins by introducing the radian measure of an angle and the arc-length relation l = rθ, then defines the six trigonometric functions — sine, cosine, tangent, cosecant, secant, and cotangent — for any real-valued angle using the unit circle. Sign conventions in all four quadrants (ASTC rule) and the values of trig functions at standard angles (0°, 30°, 45°, 60°, 90°, 180°, 270°, 360°) are covered in depth.

The heart of the chapter is the large family of trigonometric identities. Starting from the three Pythagorean identities, the chapter builds compound-angle formulas for sin(A ± B) and cos(A ± B), which in turn generate double-angle and half-angle formulas, product-to-sum (prosthaphaeresis) formulas, and sum-to-product transformations. Board questions most commonly test proof-based problems using these identities and numerical problems that require selecting the right identity chain.

The chapter closes with trigonometric equations — finding the general solution of equations such as sin x = k, cos x = k, and tan x = k. Students learn three fundamental general-solution templates and apply them to more complex equations by reducing them to a single trig ratio. This topic bridges school trigonometry with pre-calculus analysis and is a direct prerequisite for differentiation and integration of trig functions in Class 12.

Topics

What's inside Chapter 3

As per NCERT Class 11 Mathematics (CBSE syllabus)

Topic 1
Angles — Degree & Radian Measure
Definition of an angle; degree and radian as units; conversion formula π rad = 180°; arc-length relation l = rθ. Problems on converting between degree and radian measure and finding arc length or sector area.
Topic 2
Trigonometric Functions & Sign in Quadrants
Unit-circle definition of sin, cos, tan, cosec, sec, cot for all real angles. ASTC sign rule across four quadrants. Values at standard angles (0°, 30°, 45°, 60°, 90°, 180°, 270°, 360°) and allied-angle transformations (90°±θ, 180°±θ, 270°±θ).
Topic 3
Trigonometric Identities
Three Pythagorean identities; compound-angle formulas for sin(A±B), cos(A±B), tan(A±B); double-angle formulas (sin 2A, cos 2A, tan 2A); half-angle formulas; product-to-sum and sum-to-product transformations.
Topic 4
Values of Trig Functions for Specific Angles
Exact evaluation of sin, cos, tan at non-standard angles (e.g. 15°, 75°, 22.5°) using compound or half-angle formulas. Application to simplifying expressions and proving special-angle results.
Topic 5
Trigonometric Equations — General Solutions
General solution for sin x = sin α (x = nπ + (−1)ⁿα), cos x = cos α (x = 2nπ ± α), tan x = tan α (x = nπ + α), where n ∈ Z. Solving compound equations by reducing to a single trig ratio.
Connections

How this chapter fits in

Useful for setting question difficulty and cross-chapter papers.

Builds on
Class 10 · Introduction to Trigonometry
Right-triangle definitions, standard angle values, basic identities
Ch 1 · Sets (Class 11)
Domain and range of trigonometric functions as real-valued mappings
Chapter 3 Trigonometric
Functions
Leads to
Class 12 · Inverse Trigonometric Functions
Restricted domains and principal-value branches of sin⁻¹, cos⁻¹, tan⁻¹
Class 12 · Differentiation & Integration
Derivatives and integrals of all six trig functions depend on this chapter
Board Blueprint

Marks & question-type breakdown

Typical pattern based on CBSE Class 11 Mathematics annual examination papers from the last five years.

Question type Marks Typical count What's usually tested
MCQ / Assertion–Reason 1 1–2 Exact value, sign in quadrant, radian conversion, or identity recognition
Very Short Answer 2 1 Evaluate a trig function, verify a basic identity, or find arc length
Short Answer (Proof / Identity) 3 1–2 Prove compound-angle or double-angle identity; simplify expression
Long Answer (Equation / Derivation) 4–5 1 General solution of a trig equation; multi-step identity proof; exact values
Total (approximate) 8–10 4–6 Weightage varies across paper sets and years
Sample Questions

8 sample questions — generated by MarksZen AI

Aligned to CBSE Class 11 Maths Chapter 3. Covers all question types across Easy, Medium, and Hard difficulty.

Q1 Easy 1 mark MCQ
The value of sin 765° is: (a) 1/√2 (b) −1/√2 (c) √3/2 (d) 1/2
Q2 Easy 2 marks Short Answer
Convert 240° into radian measure and find the length of arc subtended by this angle in a circle of radius 6 cm.
Q3 Medium 2 marks Short Answer
If sin A = 3/5 and A lies in the second quadrant, find the values of cos A, tan A, and cosec A.
Q4 Medium 3 marks Short Answer
Prove that: cos(π/4 − x) · cos(π/4 − y) − sin(π/4 − x) · sin(π/4 − y) = sin(x + y)
Q5 Medium 3 marks Short Answer
Find the exact value of sin 75° using the compound-angle formula. Also write the value of cos 75°.
Q6 Hard 4 marks Proof
Prove the identity: (sin 3A + sin A) / (cos 3A − cos A) = −cot A State clearly each identity you use and show every step.
Q7 Hard 4 marks Trigonometric Equation
Find the general solution of: 2 cos²x + 3 sin x = 0 Clearly state the general-solution formula used and show all steps.
Q8 Hard 5 marks Word Problem
A wheel of a bicycle has radius 35 cm. It completes 20 revolutions per second. (i) Find the angle (in radians) swept by a spoke in 5 seconds. (ii) Find the distance travelled by a point on the rim in 5 seconds. (iii) Express the angle swept in degree measure.
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Previous Year Questions

From CBSE board examinations

Actual questions from past Class 11 Mathematics board and school-level examination papers — Trigonometric Functions chapter.

Board 20223 marks
Prove that: cos 6x = 32 cos⁶x − 48 cos⁴x + 18 cos²x − 1 (CBSE All India 2022)
Board 20233 marks
Find the general solution of the equation tan 2x = −cot(x + π/3). (CBSE 2023)
Board 20204 marks
Prove that: (sin 5x − 2 sin 3x + sin x) / (cos 5x − cos x) = tan x (CBSE 2020)
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  • All 5 topics of this chapter
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FAQ

Questions teachers ask

How many marks does Trigonometric Functions carry in the CBSE Class 11 Mathematics exam? +
Trigonometric Functions typically carries 8–10 marks in the CBSE Class 11 Mathematics annual examination. Questions usually include one 1-mark MCQ or assertion-reason, one 2-mark short answer on identities or exact values, one 3-mark problem on compound or allied angles, and one 4–5 mark question involving equations or proofs. The chapter's high weightage is consistent across most paper sets.
What is the radian measure system and why does CBSE Class 11 introduce it? +
The radian is the SI unit of angle measurement. One radian is the angle subtended at the centre of a circle by an arc equal in length to the radius. CBSE Class 11 introduces radians because calculus-based results (derivatives, integrals of trig functions) only hold when angles are in radians. The conversion formula is: π radians = 180°. Students are expected to convert fluently in board exams.
Which trigonometric identities are most frequently tested in CBSE Class 11 board exams? +
The most frequently tested identities are: (1) Pythagorean identities — sin²x + cos²x = 1, 1 + tan²x = sec²x, 1 + cot²x = cosec²x; (2) compound-angle formulas — sin(A ± B), cos(A ± B), tan(A ± B); (3) double-angle formulas — sin 2A = 2 sin A cos A, cos 2A = cos²A − sin²A; and (4) product-to-sum and sum-to-product transformations. Proof-based questions using these identities appear almost every year as 3–4 mark questions.
How should students approach trigonometric equation questions in board exams? +
For CBSE board questions on trigonometric equations, students should: (1) reduce the equation to a single trig ratio (sin, cos, or tan); (2) express the right-hand side as a standard exact value; (3) write the general solution using the correct formula — x = nπ + (−1)ⁿα for sine, x = 2nπ ± α for cosine, x = nπ + α for tangent; (4) state "where n ∈ Z". Most board questions are 3 marks and award one mark for each step.
How do I generate a custom question paper for Trigonometric Functions using MarksZen? +
Sign up for a free MarksZen account, choose CBSE Class 11 Mathematics, select Chapter 3 (Trigonometric Functions), set your preferred question-type mix (MCQ, short answer, proof, equation) and total marks — the AI generates a complete board-aligned paper with answer key in under 2 minutes, ready for PDF export.