1. ESCOLA SECUNDÁRIA ALBERTO SAMPAIO
TRIGONOMETRIA
FÓRMULAS - SISTEMA SEXAGÉSIMAL
30 45 60
1 2 3
sen
2 2 2
3 2 1
cos
2 2 2
3 3
tg 1
3
3
cotg 3 1
3
π π π
6 4 3
sen(90 − α ) = cos α sen(90 + α ) = cos α
cos(90 − α ) = sen α cos(90 + α) = − sen α
tg (90 − α ) = cot g α tg (90 + α ) = − cot g α
cot g (90 − α ) = tg α cot g (90 + α ) = − tg α
sen(180 − α ) = sen α sen(180 + α ) = − sen α
cos(180 − α ) = − cos α cos(180 + α ) = − cos α
tg (180 − α) = − tg α tg (180 + α) = tg α
cot g (180 − α ) = − cot g α cot g (180 + α ) = cot g α
sen(270 − α ) = − cos α sen(270 + α ) = − cos α
cos(270 − α ) = − sen α cos(270 + α ) = sen α
tg (270 − α ) = cot g α tg (270 + α ) = − cot g α
cot g (270 − α ) = tg α cot g (270 + α ) = − tg α
sen(360 − α ) = − sen α sen( − α) = − sen α
cos(360 − α ) = cos α cos( − α ) = cos α
tg (360 − α ) = − tg α tg ( − α) = − tg α
cot g (360 − α ) = − cot g α cot g ( − α ) = − cot g α
JORGE FREITAS TRIGONOMETRIA fórmulas.doc 18/10/2005

2. SISTEMA CIRCULAR
π π
sen( − α ) = cos α sen( + α ) = cos α
2 2
π π
cos( − α) = sen α cos( + α ) = − sen α
2 2
π π
tg ( − α ) = cot g α tg ( + α ) = − cot g α
2 2
π π
cot g ( − α ) = tg α cot g ( + α ) = − tg α
2 2
sen( π − α ) = sen α sen( π + α ) = − sen α
cos( π − α ) = − cos α cos( π + α ) = − cos α
tg ( π − α ) = − tg α tg ( π + α ) = tg α
cot g ( π − α ) = − cot g α cot g ( π + α ) = cot g α
3 3
sen( π − α ) = − cos α sen( π + α ) = − cos α
2 2
3 3
cos( π − α ) = − sen α cos( π + α ) = sen α
2 2
3 3
tg ( π − α ) = cot g α tg ( π + α ) = − cot g α
2 2
3 3
cot g ( π − α ) = tg α cot g ( π + α ) = − tg α
2 2
sen(2π − α ) = − sen α sen( − α) = − sen α
cos(2π − α ) = cos α cos( − α ) = cos α
tg (2π − α ) = − tg α tg ( − α) = − tg α
cot g (2π − α ) = − cot g α cot g ( − α ) = − cot g α
FÓRMULA FUNDAMENTAL DA TRIGONOMETRIA
sen 2 α + cos2 α = 1
1 1
tg 2 α = −1 cotg 2 α = −1
cos2 α sen 2 α

3. 00 300 450 600 900 1200 1350 1500 1800
π π π π 2 3 5
0 π π π π
6 4 3 2 3 4 6
2100 2250 2400 2700 3000 3150 3300 3600
7 5 4 3 5 7 11
π π π π π π π π
6 4 3 2 3 4 6