Matemática - Trigonometria

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