|
|
|
0
C
C
C
C
2
sin x
0
1
0
-1
0
cos x
1
0
-1
0
1
tg x
0
|
0
|
0
ctg x
|
0
|
0
|
Formula fundamentala:
sin
cos tg 1 ctg 1
|
sin cos tg ctgx |
tgx= ctgx= tgx= ctgx= secx= cosecx=
sin
x+cosx=1
Formule provenite din formula fundamentala:
sin cos tg sin cos ctg sin tg ctg cos tg ctg
x=
x=
x=
x=
x=
x=
x=1- cosxx=
x=
x=1- sinxx=
x=
Functii trigonometrice:
f: f: f: f: f:[-1,1] f:[-1,1] f: f:
[-1,1], f(x) = sinx[-1,1], f(x) = cosx
, f(x) =tgx
, f(x)= ctgx
, f(x)= arcsin x, f(x)= arccos x
, f(x)= arctg x
, f(x)= arcctg x
sin(-x)
= - sinx cos(-x)
= cosx tg(-x)
= - tgx ctg(-x)
= - ctgx arcsin(-x)=
-arcsin x arccos(-x)=
arctg(-x)=
-arctg x arcctg(-x)=
-arccos x-arcctg x
Paritatea si imparitatea functiilor trigonometrice:
x x x x
arcsin(sinx)=xarccos(cosx)=x
arctg(tgx)=x
arcctg(ctgx)=x
x x x x
Periodicitatea functiilor
[-1, 1]
sin(arcsinx)=x[-1, 1]cos(arccosx)=xtg(arctgx)=xctg(arcctgx)=x
trigonometrice:
sin(x+2k cos(x+2k tg(x+k ctg(x+k k
) = sinx) = cosx) = tgx) = ctgx, 
Reducerea la primul cadran: Deplasarea in punctul diametral opus:
x sinx=sin( cosx=
- cos( tgx
= - tg( ctgx
= - ctg( x sinx
= - sin(x - cosx
= - cos(x - tgx
= tg(x - ctgx
= ctg(x - x sinx
= - sin(2 cosx
= cos(2 tgx
= - tg(2 ctgx
= - ctg (2 x sin(x - cos(x - tg(x - ctg(x -
C: - x)- x)- x)- x)
C: ))))
C:- x)- x)- x)- x)
:) =sin(x+) = - sinx) = cos(x+) = - cosx) = tg(x+) = tgx) = ctg(x+) = ctgx
sin(x+y)
= sinxcosy + cosxsiny cos(x+y)
= cosxcosy - sinxsiny tg(x+y)
= ctg(x+y)
= sin(x-y)
= sinxcosy - cosxsiny cos(x-y)
= cosxcosy + sinxsiny tg(x-y)
= ctg(x-y)
= sin2x
= 2sinxcosx cos2x
= cos =2cos = 1 - 2sin tg2x
= ctg2x
= sin cos tg ctg cosx-1
= - 2sin cosx+1
= 2cos sin3x
= 3sinx - 4sin cos3x
= - 3cosx + 4cos tg3x
= ctg3x
=
x-sinx =x - 1 = x
= 
= 
= 
= 
xx
Transformarea produselor in sume: Transformarea sumelor in produse:Substitutia
sinx+siny
= 2sin sinx-siny
= 2cos cosx+cosy
= 2cos cosx-cosy
= - 2sin tgx+tgy
= cosx
cosy = sinx
cosy = sinx
siny =
; tgx-tgy = 
universala:
t
= tg sinx
= cosx
= tgx
= ctgx
= arctg
x
arctg y = arctg 
Functiile trigonometrice:
sinx
= a, a cosx
= a, a tgx
= a, a ctgx
= a, a sinx
= sina, a cosx
= cosa, a tgx
= tga, a ctgx
= ctgx, a
[-1, 1]x = (-1)
arcsin a + k, kZ[-1, 1]x = arccos a + 2k, kZRx = arctg a + k, kZRx = arcctg a+ k, kZ
Ecuatii trigonometrice:
Rx = (-1)a + k, kZRx = a + 2k, kZR
x = a+k, kZR x = a+k, kZ
arcsin
x +arccos x = arctg
x +arcctg x = sinx
= 0 cosx
= 0 tgx
= 0 ctgx
= 0
x = k, kZx = 
, kZx = k, kZx = , kZ
=cosx