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2FJ.RU

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ARCSIN a
-p/2arcsin a p/2 sin(arcsin a)=a
arcsin (-a)= -arcsin a
a 0 1/2 2/2 3/2 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 2/2 3/2 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/2arctg a p/2 tg(arctg a)=a
arctg (-a)= -arctg a
a 0 3/3 1 3
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 2/2 3/2 1 0 3/2 2/2 1/2 -1
cos 1 3/2 2/2 1/2 0 -1 -1/2 -2/2 -3/2 0
tg 0 1/3 1 3 - 0 -3 -1 -1/3 -
ctg - 3 1 1/3 0 - -1/3 -1 -3 0
sin2+cos2=1 sin=1-cos2         sin(-a)=-sina tg(-a)=-tga
tgctg=1 cos=1-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 2/2 3/2 1 0 3/2 2/2 1/2 -1
cos 1 3/2 2/2 1/2 0 -1 -1/2 -2/2 -3/2 0
tg 0 1/3 1 3 - 0 -3 -1 -1/3 -
ctg - 3 1 1/3 0 - -1/3 -1 -3 0
sin2+cos2=1 sin=1-cos2         sin(-a)=-sina tg(-a)=-tga
tgctg=1 cos=1-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)/2
tg(p/2-a)=ctga   sina-sinb=2sin(a-b)/2*cos(a+b)/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


Y = C O S x
1). D(y)=R         2). E(y)=[-1;1]
3). 2p
4).׸; cos (-x)=cos x
5). [-p+2pk;2pk], kZ

[2pk;p+2pk], kZ

6). =1 =2pk, kZ

=-1 =p=2pk, kZ

7). =p/2+pk, kZ

8).MAX =1 =2pk, kZ

MIN =-1 =p+2pk, kZ

9).x>0 [-p/2+2pk;p/2+2pk], kZ

x<0 [-p/2+2pk;p/2+2pk], kZ


Y = S I N x
1). D(y)=R         2). E(y)=[-1;1]
3). 2p
4).; sin (-x)=-sin x
5). [-p/2+2pk;p/2+2pk], kZ

[p/2+2pk;3p/2+2pk], kZ

6). =1 =p/2+2pk, kZ

=-1 =-p/2+2pk, kZ

7). =pk, kZ

8).MAX =1 =p/2+2pk, kZ

MIN =-1 =-p/2+p+2pk, kZ

9).x>0 [2pk;p+2pk], kZ

x<0 [p+2pk;2p+2pk], kZ


Y = T G x
1). D(y)-, =p/2+pk kZ

2). E(y)=R
3). p
4).; tg (-x)=-tg x
5). (-p/2+pk;p/2+pk), kZ

6). =pk, kZ

7). x>0 (pk;p/2+pk), kZ

x<0 (-p/2+pk;pk), kZ




 
 

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