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 tg•ctg=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=2sina•cosa 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)=sin•cos tg2a=2tga/1-tga cos(a+b)=cosa•cosb-sina•sinb sin3a=3sina-4sin3a cos(a-b)=cosa•cosb+sina•sinb cos3a=4cos3a-3cosa sin(a+b)=sina•cosb+cosa•sinb tg(a+b)=tga+tgb
sin(a-b)=sina•cosb-cosa•sinb 1-tga•tgb 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 |
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 |
|
|