Chapter 3 — Trigonometric Functions

Chapter 3 of the Class 11 Maths NCERT textbook, "Trigonometric Functions", extends trigonometric ratios to all real angles using radian and degree measures, defining six functions from unit-circle coordinates with applications in physics, engineering, navigation, and seismology.

• Measuring angles and the unit circle — The chapter generalises angles beyond triangles using degree and radian measure, then places them on the unit circle so that any real angle gets coordinates — the move that turns trigonometric ratios into full functions of real numbers.
• Identities that relate the functions — Starting from the fundamental identity, it derives addition, subtraction, double-angle and product-to-sum formulas, giving a connected toolkit for rewriting and simplifying trigonometric expressions rather than a list of isolated facts.
• Behaviour across the quadrants — All six functions are analysed for their domains, ranges, signs and periodic behaviour across the four quadrants, so you can predict how each function moves and repeats rather than just evaluate it at a point.

1. 01Angle measurement: degree (1/360 revolution) and radian (arc length / radius in unit circle) related by π rad = 180°
2. 02Trigonometric functions defined via unit circle: cos x = x-coordinate, sin x = y-coordinate, with fundamental identity sin²x + cos²x = 1
3. 03Domain and range: sin/cos defined for all reals with range [−1, 1]; tan/cot defined except at odd multiples of π/2 and multiples of π respectively
4. 04Addition formulas: cos(x+y) = cos x cos y − sin x sin y; sin(x+y) = sin x cos y + cos x sin y; tan(x+y) = (tan x + tan y)/(1 − tan x tan y)
5. 05Double-angle formulas: sin 2x = 2 sin x cos x; cos 2x = cos²x − sin²x = 2cos²x − 1 = 1 − 2sin²x; tan 2x = 2tan x/(1 − tan²x)
6. 06Sum-to-product: cos x + cos y = 2cos((x+y)/2)cos((x−y)/2); sin x + sin y = 2sin((x+y)/2)cos((x−y)/2)