6/7/2019 Year 2 Mathematics Formulas (Edexcel) - Google Docs
Highlighted formulas are not given in the formula booklet
Degrees and radians
degrees 0 30 45 60 90 120 180 270 360
π π π π 2π 3π
radians 0 6 4 3 2 3 π 2 2π
Radians to degrees: divide by π, multiple by 180
Degrees to radians: divide by 180, multiple by π
Circles:
Arc length, s: s = rθ
Sector area: A = 21 r 2 θ
Small angle approximations:
sinθ ≈ θ
cosθ ≈ 1 − 21 θ 2
tanθ ≈ θ
Special angles:
x (deg) x (rad) Sin x Cos x Tan x
0 0 0 1 0
π 1 √3 1
30 6 2 √3
2
π 1 1
45 4 √2 √2
1
π √3 1
60 3 2 2 √3
π
90 2 1 0 -
180 π 0 -1 0
Cosec sec and cot:
1
cosecθ ≡ sinθ
1
secθ ≡ cosθ
1
cotθ ≡ tanθ
Trig identities:
cos2 θ + sin2 ≡ 1
tanθ ≡ sinθ
cosθ
sec2 θ ≡ 1 + tan2 θ
cosec2 θ ≡ 1 + cot2 θ
A∓B
sinA ± sinB = 2 sin A±B 2 cos 2
cosA + cosB = 2 cos A+B A−B
2 cos 2
cosA − cosB = 2 sin A+B A−B
2 sin 2
The addition formulas:
sin(A ± B ) ≡ sinAcosB ± cosAsinB
cos(A ± B ) ≡ cosAcosB sinAsinB∓
tan(A ± B ) ≡ 1tanA±tanB
∓tanAtanB
https://docs.google.com/document/d/1jgnEixHUjpfKWER4h2LdKVwngPlqi756_BO7cs3pbTU/edit 1/4
Highlighted formulas are not given in the formula booklet
Degrees and radians
degrees 0 30 45 60 90 120 180 270 360
π π π π 2π 3π
radians 0 6 4 3 2 3 π 2 2π
Radians to degrees: divide by π, multiple by 180
Degrees to radians: divide by 180, multiple by π
Circles:
Arc length, s: s = rθ
Sector area: A = 21 r 2 θ
Small angle approximations:
sinθ ≈ θ
cosθ ≈ 1 − 21 θ 2
tanθ ≈ θ
Special angles:
x (deg) x (rad) Sin x Cos x Tan x
0 0 0 1 0
π 1 √3 1
30 6 2 √3
2
π 1 1
45 4 √2 √2
1
π √3 1
60 3 2 2 √3
π
90 2 1 0 -
180 π 0 -1 0
Cosec sec and cot:
1
cosecθ ≡ sinθ
1
secθ ≡ cosθ
1
cotθ ≡ tanθ
Trig identities:
cos2 θ + sin2 ≡ 1
tanθ ≡ sinθ
cosθ
sec2 θ ≡ 1 + tan2 θ
cosec2 θ ≡ 1 + cot2 θ
A∓B
sinA ± sinB = 2 sin A±B 2 cos 2
cosA + cosB = 2 cos A+B A−B
2 cos 2
cosA − cosB = 2 sin A+B A−B
2 sin 2
The addition formulas:
sin(A ± B ) ≡ sinAcosB ± cosAsinB
cos(A ± B ) ≡ cosAcosB sinAsinB∓
tan(A ± B ) ≡ 1tanA±tanB
∓tanAtanB
https://docs.google.com/document/d/1jgnEixHUjpfKWER4h2LdKVwngPlqi756_BO7cs3pbTU/edit 1/4
