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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