Relation Between Degree & Radian

Since a circle subtends at the centre an angle whose radian measure is 2π and its degree measure is 360°,

2π radian = 360°

π radian = 180°

Trigonometric Functions

Trigo Formulae

  1. Sin2A + cos2A = 1
  2. Sec2A - tan2A = 1
  3. Cosec2A - cot2A = 1

Trigonometric Identities

sin (– x) = – sin x

cos (– x) = cos x

cos (x + y) = cos x cos y – sin x sin y

cos (x – y) = cos x cos y + sin x sin y

cos (π/2 – x) = sin x

sin (π/2 – x) = cos x

sin (x + y) = sin x cos y + cos x sin y

sin (x – y) = sin x cos y – cos x sin y

cos (π/2 + x) = – sin x

sin (π/2 + x) = cos x

cos (π – x) = – cos x

sin (π – x) = sin x

cos (π + x) = – cos x

sin (π + x) = – sin x

cos (2π – x) = cos x

sin (2π – x) = – sin x

tan (x + y) = (tan x + tan y)/(1 - tan x tan y)

tan (x - y) = (tan x - tan y)/(1 + tan x tan y)

cot (x + y) = (cot x cot y - 1)/(cot y + cot x)

cot (x - y) = (cot x cot y + 1)/(cot y - cot x)

cos 2x = cos2 x – sin2 x = 2 cos2 x – 1 = 1 – 2 sin2 x = (1 - tan2 x)/(1 + tan2 x)

sin 2x = 2 sin x cos x = (2 tan x)/(1 + tan2 x)

tan 2x = (2 tan x)/(1 - tan2 x)

sin 3x = 3 sin x – 4 sin3 x

cos 3x = 4 cos3 x – 3 cos x

tan 3x = (3 tan x - tan3 x)/(1 - 3 tan2 x)

cos x + cos y = 2 cos (x+y)/2 cos (x-y)/2

cos x – cos y = – 2 sin (x+y)/2 sin (x-y)/2

sin x + sin y = 2 sin (x+y)/2 cos (x-y)/2

sin x – sin y = 2 cos (x+y)/2 sin (x-y)/2

Inverse Trigonometric Functions

y = sin–1 x ⇒ x = sin y

x = sin y ⇒ y = sin–1 x

sin (sin–1 x) = x

sin–1 (sin x) = x

sin–1 1/x = cosec–1 x

cos–1 (–x) = π – cos–1 x

cos–1 1/x = sec–1 x

cot–1 (–x) = π – cot–1 x

tan–1 1/x = cot–1 x

sec–1 (–x) = π – sec–1 x

sin–1 (–x) = – sin–1 x

tan–1 (–x) = – tan–1 x

tan–1 x + cot–1 x = π/2

cosec–1 (–x) = – cosec–1 x

sin–1 x + cos–1 x = π/2

cosec–1 x + sec–1 x = π/2

tan–1 x + tan–1 y = tan–1 (x+y)/(1-xy)

2 tan–1 x = tan–1 (2x)/(1-x2)

tan–1 x – tan–1 y = tan–1 (x-y)/(1+xy)

2 tan–1 x = sin–1 (2x)/(1+x2) = cos–1 (1-x2)/(1+x2)