Upload
geometria-ensino-medio
View
663
Download
0
Embed Size (px)
Citation preview
ESCOLA SECUNDÁRIA ALBERTO SAMPAIO TRIGONOMETRIA
FÓRMULAS - SISTEMA SEXAGÉSIMAL
JORGE FREITAS TRIGONOMETRIA fórmulas.doc 18/10/2005
30 45 60
sen 12
22
3
2
cos
32
2
2
12
tg 3
3
1
3
cotg
3
1
33
π6
π4
π3
sen( ) cos90 − =α α sen( ) cos90 + =α α
cos( )90 − =α αsen cos( )90 + = −α αsen
tg g( ) cot90 − =α α tg g( ) cot90 + = −α α
cot ( )g tg90 − =α α cot ( )g tg90 + = −α α
sen sen( )180 − =α α sen sen( )180 + = −α α
cos( ) cos180 − = −α α cos( ) cos180 + = −α α
tg tg( )180 − = −α α tg tg( )180 + =α α
cot ( ) cotg g180 − = −α α cot ( ) cotg g180 + =α α
sen( ) cos270 − = −α α sen( ) cos270 + = −α α
cos( )270 − = −α αsen cos( )270 + =α αsen
tg g( ) cot270 − =α α tg g( ) cot270 + = −α α
cot ( )g tg270 − =α α cot ( )g tg270 + = −α α
sen sen( )360 − = −α α sen sen( )− = −α α
cos( ) cos360 − =α α cos( ) cos− =α α
tg tg( )360 − = −α α tg tg( )− = −α α
cot ( ) cotg g360 − = −α α cot ( ) cotg g− = −α α
SISTEMA CIRCULAR
sen( ) cosπα α
2− =
sen( ) cosπ
α α2+ =
cos( )πα α
2− = sen
cos( )π
α α2+ = − sen
tg g( ) cotπα α
2− =
tg g( ) cotπ
α α2+ = −
cot ( )g tgπα α
2− =
cot ( )g tgπ
α α2+ = −
sen sen( )π α α− = sen sen( )π α α+ = − cos( ) cosπ α α− = − cos( ) cosπ α α+ = − tg tg( )π α α− = − tg tg( )π α α+ =
cot ( ) cotg gπ α α− = − cot ( ) cotg gπ α α+ =
sen( ) cos32π α α− = −
sen( ) cos3
2π α α+ = −
cos( )32π α α− = − sen
cos( )3
2π α α+ = sen
tg g( ) cot32π α α− =
tg g( ) cot3
2π α α+ = −
cot ( )g tg32π α α− =
cot ( )g tg3
2π α α+ = −
sen sen( )2π α α− = − sen sen( )− = −α α cos( ) cos2π α α− = cos( ) cos− =α α tg tg( )2π α α− = − tg tg( )− = −α α
cot ( ) cotg g2π α α− = − cot ( ) cotg g− = −α α FÓRMULA FUNDAMENTAL DA TRIGONOMETRIA sen cos2 2 1α α+ =
tg22
1 1αα
= −cos
cotg
sen2
2
1 1αα
= −
00 300 450 600 900 1200 1350 1500 1800 0
π6
π4
π3
π2
23π
34π
56π
π
2100 2250 2400 2700 3000 3150 3300 3600 76π
54π
43π
32π
53π
74π
116π
π