Formule trigonometrice

Formule trignometrice 1
FORMULE TRIGONOMETRICE








Formula fundamentala:













Formule provenite din formula fundamentala:








Func?ii trigonometrice:







Paritatea si imparitatea functiilor trigonometrice:




Periodicitatea functiilor
trigonometrice:




tgx=
x
x
cos
sin

ctgx=
x
x
sin
cos

tgx=
ctx
1

ctgx=
tgx
1

secx=
xcos
1

cosecx=
xsin
1


sin 2 x+cos 2 x=1
cos 2 x=1- sin 2 x
tg 2 x=
x
x
2
2
sin1
sin
?
ctg 2 x=
x
x
2
2
sin
sin1?

sin 2 x=
xtg
xtg
2
2
1+
cos 2 x=
xtg 21
1
+
ctg 2 x=
xtg 2
1

sin 2 x=1- cos 2 x
tg 2 x=
x
x
2
2
cos
cos1?

ctg 2 x=
x
x
2
2
cos1
cos
?
sin 2 x=
xctg 21
1
+
cos 2 x=
xctg
xctg
2
2
1+
tg 2 x=
xctg 2
1

sin ??
???
? ? x
2
?
=cosx
cos ??
???
? ? x
2
?
=sinx
tg ??
???
? ? x
2
?
=ctgx
ctgx ??
???
? ? x
2
?
=tgx
0 C I
2
?
C II
? C III
2
3?
C IV
2?
sin x 0 + 1 + 0 - -1 - 0
cos x 1 + 0 - -1 - 0 + 1
tg x 0 + ? | ?? - 0 + ? | ?? - 0
ctg x |? + 0 - ?? |? +0- ?? |

6
?

4
?

3
?

sin
2
1

2
2

2
3

cos
2
3

2
2
2
1

tg
3
3

1 3
ctg 3 1
3
3

x ,
22
?????? ?????arcsin(sinx)=x
x ,
22
?????? ?????arccos(cosx)=x
x ;
22
?????? ?????arctg(tgx)=x
x ()0; ???arcctg(ctgx)=x
sin(x+2k? ) = sinx
cos(x+2k? ) = cosx
tg(x+k? ) = tgx
ctg(x+k? ) = ctgx,
k? Z
f: ?? [-1,1], f(x) = sinx
f: ?? [-1,1], f(x) = cosx
f: ? ???
?
??
? ?+ Zkk /
2
?? ? , f(x) =tgx
f: ? {}Zkk ?/? ? ? , f(x)= ctgx
arcsin(-x)= -arcsin x
arccos(-x)= ? -arccos x
arctg(-x)= -arctg x
arcctg(-x)= ? -arcctg x
f:[-1,1] ? ? , f(x)= arcsin x
f:[-1,1] ? ? , f(x)= arccos x
f: ;
22
??????????? , f(x)= arctg x
f: ( )0; ? ? ? , f(x)= arcctg x
sin(-x) = - sinx
cos(-x) = cosx
tg(-x) = - tgx
ctg(-x) = - ctgx
x?[-1, 1]? sin(arcsinx)=x
x?[-1, 1]? cos(arccosx)=x
x? ? ? tg(arctgx)=x
x? ? ? ctg(arcctgx)=x
Formule trignometrice 2
Reducerea la primul cadran: Deplasarea in punctul diametral opus:

























Transformarea produselor in sume: Transformarea sumelor in produse: Substitutia
universala:










Functiile trigonometrice:
Ecuatii trigonometrice:








x?C II :
sinx=sin(? - x)
cosx= - cos(? - x)
tgx = - tg(? - x)
ctgx = - ctg(? - x)
x?C III :
sinx = - sin(x - ? )
cosx = - cos(x - ?
)
tgx = tg(x - ? )
x...