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Trigonometric Functions

NCERT Class 11 Mathematics Chapter 3

Trigonometric Functions for Class 11 Maths and JEE: radian measure, signs, domain and range, graphs, and sum, difference and multiple-angle formulas.

3 topics Updated 8 Nov 2026

For: Class 11 and JEE

In the syllabus: JEE Class 11 syllabus

With your textbook

NCERT Mathematics (Class 11), Chapter 3 “Trigonometric Functions”, reprint 2026-27.

Open the official NCERT chapter (PDF, 3.0 MB, ncert.nic.in)

Checked on 19 Oct 2026.

Learn in this order

  1. Angles: degree and radian measure

    What a radian is, arc length l = rθ and the radian to degree conversion formula, with solved examples.

    NCERT Section 3.2 11 min read 5 solved examples 9 practice questions

  2. Trigonometric functions

    Trigonometric functions for Class 11 Maths and JEE: the unit circle, values table, signs in each quadrant (ASTC), domain, range and graphs of all six.

    NCERT Section 3.3 17 min read 5 solved examples 9 practice questions

  3. Sum and difference formulas

    Allied, double, triple and half angles, sum-to-product, with proofs.

    NCERT Section 3.4 20 min read 6 solved examples 10 practice questions

Key formulas in this chapter

Angles

  • π radian = 180°; 2π radian = 360°
  • radians = (π/180) × degrees
  • degrees = (180/π) × radians
  • l = rθ, θ in radians
  • 1° = 60′, 1′ = 60″

Trigonometric functions

  • cos x = a, sin x = b for P(a, b) on the unit circle
  • sin x + cos x = 1
  • 1 + tan x = sec x; 1 + cot x = cosec x
  • sin (2nπ + x) = sin x
  • cos (2nπ + x) = cos x
  • sin x = 0 ⇔ x = nπ; cos x = 0 ⇔ x = (2n + 1)π/2
  • cos (−x) = cos x; sin (−x) = −sin x

Sum and difference formulas

  • cos (x ± y) = cos x cos y ∓ sin x sin y
  • sin (x ± y) = sin x cos y ± cos x sin y
  • sin 2x = 2 sin x cos x
  • cos 2x = 2 cos x − 1 = 1 − 2 sin x
  • tan 2x = 2 tan x/(1 − tan x)
  • sin 3x = 3 sin x − 4 sin x
  • cos 3x = 4 cos x − 3 cos x
  • cos x + cos y = 2 cos A cos B
  • sin x + sin y = 2 sin A cos B
  • A = (x + y)/2; B = (x − y)/2

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