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StudentHelp, , MS Word. , , antiplagiat.ru, etxt.ru advego.ru. StudentHelp , Word .


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: . : 31.05.2012. : 2010. : 3. antiplagiat.ru: < 30%

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sin cos
sin(ab)=sin acosbsinbcosa
cos(ab)=cosacosb`+sin a sinb
tg a tg b
tg (ab) = 1 tg a tg b
tg (ab) =
= ctg a ctg b`+ 1 = 1 tg a tg b
ctg b ctg a tg a tg b

sin2x=2sinx cosx
cos 2x = cos2x - sin2x=
= 2cos2x-1=1-2sin2x
tg2x= 2 tgx
1 - tg2x
sin 3x =3sin x - 4 sin3x
cos 3x= 4 cos3 x - 3 cos
: , - x:
sin x= 1-cosx
2
cos x= 1+cosx
2
NB! 0 , (tg, ctg)
tg x=sinx =1-cosx = 1-cosx
1+cosx sinx 1+cosx
tg x=sinx =1+cosx = 1+cosx
1-cosx sinx 1-cosx
:
sin2 x = 1 cos 2x
2
cos2 x = 1+ cos 2x
2
sin3 x = 3 sin x sin 3x
4
cos3 x = 3 cos x + cos 3x
4
:
2 sinx siny = cos(x-y) cos(x+y)
2 cosx cosy = cos(x-y)+cos(x+y)
2 sinx cosy = sin(x-y) + sin (x+y)
tgx tgy = tgx + tgy
ctgx + ctgy
ctgx ctgy = ctgx + ctgy
tgx + tgy
tgx ctgy = tgx + ctgy
ctgx + tgy
NB! 0 , (tg, ctg)




sinx siny= 2sin xy cos x`+ y
2 2
cosx + cosy =2cos x+y cos x-y
2 2
cosx - cosy = - 2sin x+y sin x-y
2 2
tgx tgy= sin(xy)
cosx cosy
tgx + tgy = cos(x-y)
cosx siny
ctgx - tgy = cos(x+y)
sinx cosy
ctgxctgy= sin(yx)
sinx siny
sin x = 1 x= p +2pn, n Z
sin x = 0 x= pn, n Z
sin x = -1 x= - p +2pn, n Z
sin x = a , [a] 1
x = (-1)karcsin a + pk, k Z
cosx=1 x=2pn, n Z
cosx=0 x= p +pn, n Z
cosx= -1 x=p +2pn, n Z
cosx= - x=2/3 p +2pn, n Z
cosx = a , [a] 1
x=arccos a + 2pn, n Z
arccos(-x)= p- arccos x
arcctg(-x)= p - ctg x
tg x= 0 x= n, n Z
ctg x= 0 x= p+ p n, n Z
tg x= ax= arctg a +pn, n Z
ctg x = ax=arcctg a + pn, n Z
:
\f(a) sin cos tg ctg
I + + + +
II + - - -
III - - + +
IY - + - +
a =p a/180; a=a 180/p

a p/2 a p a 3/2 p a 2p a
sin -sin a cos a `+sin a - cos a - sin a
cos cos a `+sin a - cos a sin a cos a
tg - tg a `+ ctg a tg a `+ ctg a - tg a
ctg - ctg a `+ tg a ctg a `+ tg a -ctg a


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