LISTS OF AMA TRIG FORMULAE

AMATHS FORMULAE

ADDITION FORMULA

Sin (A+B) = sinAcosB + cosAsinB

Sin (A- B) = sinAcosB – cosAsinB

Cos (A+B) = cosAcosB – sinAsinB

Cos (A- B) = cosAcosB + sinAsinB

Tan (A+B) =
tanA + tanB
1-tanAtanB

Tan (A- B) =
tanA- tanB
1+tanAtanB

MULTIPLE ANGLE FORMULA

Sin 2A = 2sinAcosA

Cos 2A = cos²A - sin²A
= 1 – 2sin²A
= 2cos²A – 1

Tan 2A =
2tanA
1 - tan²A

R-FORMULA
acosө + bsinө ≡ R cos (ө - α)
acosө - bsinө ≡ R cos (ө + α)
asinө + bcosө ≡ R sin (ө + α)
asinө - bcosө ≡ R sin (ө - α)

where R = √a² +b² R>0
tanα = b/a α is acute

FACTOR FORMULAE
Sin X + sin Y = 2sin X+Y cos X-Y
_________________2 _______2

Sin X – sin Y = 2cos X+Y sin X-Y
_________________2 _______2

Cos X + cos Y = 2sin X+Y sin X-Y
_________________2 _______2

Cos X – cos Y = 2sin X+Y sin Y-X
_________________2 _______2


SPECIAL ANGLES (imagine the axises)
[ I QUADRANT]
Sin90 = 1
Cos90 = 0
Tan90 = ∞


[ II QUADRANT]
Sin180 = 0
Cos180 = -1
Tan180 = 0

[ IV QUADRANT]
Sin 0 = 0
Cos 0 =1
Tan 0 = 0



[ III QUADRANT]
Sin270 = -1
Cos 270 = 0
Tan 270 = ∞


SIMPLE TRIG IDENTITIES AND EQUATION

Tan θ =
sinθ
Cosθ

Cot θ =
cosθ
Sinθ

sin²θ + cos²θ = 1
tan²θ + 1 = sec²θ
cot²θ + 1 = cosec²θ





this list is not compiled by neither mrs phillip nor ama rep.

--lois