Trigonometry Formulas
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ScribdTranslationsMATHEMATICS PHYSICS Unit 6
TRIGONOMETRICFORMULAS
you2 α+cos2α=1
tgα=, senα
cosα ≠0
cosα
cotgα= cosα
senα ,
sinα ≠ 0
cosecα=youα , sinα ≠
1 0
Identities for sums and differences
sin(±β)=sine alpha cosine beta ± sine beta cosine
cos ( ) cos αcosβαm±seven=αsenβ
tan(α) ± tan(β)
tg(α±β)= , tgαtgβ ≠ 1
1 mtgαtgβ
Identities for the double angle
sin 2α=2 sinαcosα
cos 2 1 − 2 α s e = n 2α
cos 2α=2cos2 α − 1
2 tgα
tg 2α= 2 , tgα ≠ 1
1-tgα
Identities for products, sums and differences of sine and cosine
1
he .cos =[you α)+βse+n(αα − β)β]
2
1
cos .sin [sin(α=β)β - sin(α+ - β) ]
2
1
.cos [ α) + βco + s(αα - β)β
=cos( ]
2
1 cos(α α) - β - βc = os(+αβ)
you .you [ ]
2
sinα + sinβ = 2 sin
β α+− β
cos
2 2
β α+− β
senα - senβ = 2 cos you
2 2
cosα + cosβ = 2 cos
β α+− β
cos
2 2
β α+− β
cos nis2-=
β
acos you
2 2
UTNFRBA 215
UNIVERSITY SEMINAR MODULE B
Reducoitnformuals
sen(- ) = -seαnα you( π2 ) =c−osαα
cos(-x) = cos(x) cos ( π2 ) =s−enαα
tg (- ) = -tgαα tg ( π2 ) =co−tgαα
you( π2 ) =cosαα+ sen( - ) = πseαnα
cos ( π2 ) =α−+nsiα cos(-) = π - cosαsα
( π2 ) =α−+cogtα tg ( - ) = π - tgαα
SnieandCosnieTheorems
Δ
SeaA B C
Sine theorem:
a
senα = b
senβ = c
senγ
Cosine theorem:
a 2= b 2+ 2-2bccosα
b 2= a 2+ c 2-2accosβ
c 2= a 2+ b 2-2abcosγ
216 UTNFRBA