• 
 • 
 • 
 • 
 • 
 • 
 • 
 • 
 • 
 • 
 • 
 • 
 • 
 • 
 • 
 • 
 • 
 • 
 • 
 • 
 • 
 • 
 • 
 • 
 • 
 • 
 • 
 • 
 • 
 • 
 • 
 • 
 • 
 • 
 • 
 • 
 • 
 • 





ARCSIN a
-p/2£arcsin a £p/2 sin(arcsin a)=a
arcsin (-a)= -arcsin
a a 0 1/2 Ö2/2 Ö3/2 1 arcsin a 0 p/6 p/4 p/3 p/2
SIN X= A
x=(-1)n arcsin a +pk sin x=0 x=pk sin x=1 x=p/2+2pk sin x=-1 x=-p/2+2pk
ARCCOS a
0 £arccos a £p cos(arccos a)=a
arccos (-a)=p -arccos a a 0 1/2 Ö2/2 Ö3/2 1 arccos a p/2 p/3 p/4 p/6 0
COS X= A
x= arccos a +2pk cos x=0 x=p/2+pk cos x=1 x=2pk cos x=-1 x=p+2pk
ARCTG a
-p/2£arctg a £p/2 tg(arctg a)=a
arctg (-a)= -arctg a a 0 Ö3/3 1 Ö3 tg a 0 p/6 p/4 p/3
TG X= A
x= arctg a +pk
sina*cosb=1/2[sin(a-b)+sin(a+b)]
sina*sinb=1/2[cos(a-b)-cos(a+b)]
cosa*cosb=1/2[cos(a-b)+cos(a+b)]
sina*cosb=1/2[sin(a-b)+sin(a+b)]
sina*sinb=1/2[cos(a-b)-cos(a+b)]
cosa*cosb=1/2[cos(a-b)+cos(a+b)]
sina+sinb=2sin(a+b)/2 * cos(a-b)/2
sina-sinb=2sin(a-b)/2 * cos(a+b)/2
cosa+cosb=2cos(a+b)/2 * cos(a-b)/2
cosa-cosb=-2sin(a+b)/2 * sin(a-b)/2
(a+b)2=a2+2ab+b2
(a-b)2=a2+2ab+b2
(a+b+c)2=a2+b2+c2+2ab+2ac+2bc
a2-b2=(a-b)(a+b)
(a+b)3=a3+3a2b+3ab2+b3
(a-b)3=a3-3a2b+3ab2-b3
a3+b3=(a+b)(a2-ab+b2)
a3-b3=(a-b)(a2+ab+
b2) 0 p/6 p/4 p/3 p/2 p 2/3p 3/4p 5/6p 3/2p 0 30 45 60 90 180 120 135 150 270 sin 0 1/2 Ö2/2 Ö3/2 1 0 Ö3/2 Ö2/2 1/2 -1 cos 1 Ö3/2 Ö2/2 1/2 0 -1 -1/2 -Ö2/2 -Ö3/2 0 tg 0 1/Ö3 1 Ö3 - 0 -Ö3 -1 -1/Ö3 - ctg - Ö3 1 1/Ö3 0 - -1/Ö3 -1 -Ö3 0
sin2+cos2=1 sin=Ö1-cos2 sin(-a)=-sina tg(-a)=-tga
tgctg=1 cos=Ö1-sin2 cos(-a)=cosa ctg(-g)=-ctga
tg=1/ctg ctg=1/tg 1+tg2=1/cos2=sec2
sin2=(1-cos)(1+cos) 1+ctg2=1/sin2=cosec2 sin2a=2sinacosa
cos2=(1-sin)(1+sin) 1-tg2/(1+tg2)=cos4-sin4 cos2a=cos2 a-sin2 a
cos/(1-sin)=1+sin/cos 1/(tg+ctg)=sincos tg2a=2tga/1-tga
cos(a+b)=cosacosb-sinasinb sin3a=3sina-4sin3a
cos(a-b)=cosacosb+sinasinb cos3a=4cos3a-3cosa
sin(a+b)=sinacosb+cosasinb tg(a+b)=tga+tgb
sin(a-b)=sinacosb-cosasinb 1-tgatgb
2cos2a/2=1+cosa 2sin2a/2=1-cosa 0 p/6 p/4 p/3 p/2 p 2/3p 3/4p 5/6p 3/2p 0 30 45 60 90 180 120 135 150 270 sin 0 1/2 Ö2/2 Ö3/2 1 0 Ö3/2 Ö2/2 1/2 -1 2cos2a/2=1+cosa 2sin2a/2=1-cosa cos 1 Ö3/2 Ö2/2 1/2 0 -1 -1/2 -Ö2/2 -Ö3/2 0 tg 0 1/Ö3 1 Ö3 - 0 -Ö3 -1 -1/Ö3 - ctg - Ö3 1 1/Ö3 0 - -1/Ö3 -1 -Ö3 0
sin2+cos2=1 sin=Ö1-cos2 sin(-a)=-sina tg(-a)=-tga
tgctg=1 cos=Ö1-sin2
cos(-a)=cosa ctg(-g)=-ctga
tg=1/ctg ctg=1/tg 1+tg2=1/cos2=sec2
sin2=(1-cos)(1+cos) 1+ctg2=1/sin2=cosec2 sin2a=2sinacosa
cos2=(1-sin)(1+sin) 1-tg2/(1+tg2)=cos4-sin4 cos2a=cos2 a-sin2 a
cos/(1-sin)=1+sin/cos 1/(tg+ctg)=sincos tg2a=2tga/1-tga
cos(a+b)=cosacosb-sinasinb sin3a=3sina-4sin3a
cos(a-b)=cosacosb+sinasinb cos3a=4cos3a-3cosa
sin(a+b)=sinacosb+cosasinb tg(a+b)=tga+tgb
sin(a-b)=sinacosb-cosasinb 1-tgatgb
sin(2p-a)=-sina sin(3p/2-a)=-cosa
cos(2p-a)=cosa cos(3p/2-a)=-sina
tg(2p-a)=-tga tg(3p/2-a)=ctga
sin(p-a)=sina ctg(3p/2-a)=tga
cos(p-a)=-cosa sin(3p/2+a)=-cosa
sin(p+a)=-sina cos(3p/2+a)=sina
cos(p+a)=-cosa tg(p/2+a)=-ctga
sin(p/2-a)=cosa ctg(p/2+a)=-tga
cos(p/2-a)=sina sina+sinb=2sin(a+b)/2cos(a-b)[...1]/2
tg(p/2-a)=ctga sina-sinb=2sin(a-b)/2*cos(a+b)[...2]/2
ctg(p/2-a)=tga cosa+cosb=2cos(a+b)/2cos(a-b)/2
sin(p/2+a)=cosa cosa-cosb=-2sin(a+b)/2sin(a-b)/2
cos(p/2+a)=-sina
[...1]
[...2]
Y = C O S
x
1).Ԡ D(y)=R 2).Ǡ
E(y)=[-1;1]
3).
2p
4).׸;
cos (-x)=cos x
5).
[-p+2pk;2pk],
kÎZ
[2pk;p+2pk],
kÎZ
6).
=1 =2pk, kÎZ

=-1 =p=2pk,
kÎZ
7).
=p/2+pk,
kÎZ
8).MAX
=1 =2pk, kÎZ
MIN =-1 =p+2pk,
kÎZ
9).x>0
[-p/2+2pk;p/2+2pk],
kÎZ
x<0 [-p/2+2pk;p/2+2pk],
kÎZ
Y =
S I N x
1).Ԡ D(y)=R 2).Ǡ
E(y)=[-1;1]
3).
2p
4).;
sin (-x)=-sin x
5).
[-p/2+2pk;p/2+2pk],
kÎZ
[p/2+2pk;3p/2+2pk],
kÎZ
6).
=1 =p/2+2pk,
kÎZ

=-1 =-p/2+2pk,
kÎZ
7).
=pk, kÎZ
8).MAX
=1 =p/2+2pk,
kÎZ
MIN =-1 =-p/2+p+2pk,
kÎZ
9).x>0
[2pk;p+2pk],
kÎZ
x<0 [p+2pk;2p+2pk],
kÎZ
Y =
T G x
1).Ԡ D(y)-, =p/2+pk
kÎZ
2).Ǡ E(y)=R
3).
p
4).;
tg (-x)=-tg x
5).
(-p/2+pk;p/2+pk),
kÎZ
6).
=pk, kÎZ
7). x>0
(pk;p/2+pk),
kÎZ
x<0 (-p/2+pk;pk),
kÎZ

. . . . . . . . . . . . . . .

      ©2010