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