Trigonometry formulas pdf
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Trigonometry is a branch of mathematics that deals with triangles. Trigonometry is also known as the study of relationships between lengths and angles of triangles.
1. Basic Knowledge Of trigonometry
sin θ = Opposite Side/Hypotenuse
cos θ = Adjacent Side/Hypotenuse
tan θ = Opposite Side/Adjacent Side
cot θ = Adjacent Side/Opposite Side
sec θ = Hypotenuse/Adjacent Side
cosec θ = Hypotenuse/Opposite Side
2. Reciprocal Identities
sin θ = 1/cosec θ
cos θ = 1/sec θ
tan θ = 1/cot θ
cot θ = 1/tan θ
sec θ = 1/cos θ
cosec θ = 1/sin θ
3. Co-function Identities
sin(90°−x) = cos x
cos(90°−x) = sin x
tan(90°−x) = cot x
cot(90°−x) = tan x
sec(90°−x) = csc x
cosec(90°−x) = sec x
4. Sum & Difference Identities
sin(x+y) = sin(x)•cos(y)+cos(x)•sin(y)
sin(x–y) = sin(x)•cos(y)–cos(x)•sin(y)
cos(x+y) = cos(x)•cos(y)–sin(x)•sin(y)
cos(x–y) = cos(x)•cos(y) + sin(x)•sin(y)
tan(x+y) = (tan x + tan y)/ (1−tan x•tan y)
tan(x−y) = (tan x–tan y)/ (1+tan x•tan y)
5.Periodicity Identities
sin (π/2 – A) = cos A
cos (π/2 – A) = sin A
sin (π/2 + A) = cos A
cos (π/2 + A) = – sin A
sin (3π/2 – A) = – cos A
cos (3π/2 – A) = – sin A
sin (3π/2 + A) = – cos A
cos (3π/2 + A) = sin A
sin (π – A) = sin A
cos (π – A) = – cos A
sin (π + A) = – sin A
cos (π + A) = – cos A
sin (2π – A) = – sin A
cos (2π – A) = cos A
sin (2π + A) = sin A
cos (2π + A) = cos A
6. Double Angle Identities
sin(2x) = 2sin(x) • cos(x)
sin(2x) = [2tan x/(1+tan2 x)]
cos(2x) = cos2(x)–sin2(x)
Cos(2x) = [(1-tan2 x)/(1+tan2 x)]
cos(2x) = 2cos2(x)−1
Cos(2x) = 1–2sin2(x)
tan(2x) = [2tan(x)]/ [1−tan2(x)]
sec (2x) = sec2 x/(2-sec2 x)
cosec (2x) = (sec x. cosec x)/2
7. Triple Angle Identities
Sin 3x = 3sin x – 4sin3x
Cos 3x = 4cos3x-3cos x
Tan 3x = [3tanx-tan3x]/[1-3tan2x]
8. half angle formula trigonometry
9. Product identities
10. Sum to product identities
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