y=arccos(x). 3.
: - .
3.1. ϳ
3.1.1.
, , . , - . - . , . . . .
. ', . . , . , . . , , ( ), (.1)
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3.2.
3.2.1. ,
arccos a , .
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2. ;
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3.2.2. ³ ,
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4.
cos x = , ǀ a ǀ ≤ 1,
5.
41.1.
, , , . , , , .
cos x = 1 , , cos 360 = 1, cos 720 = 1, cos - 360 = 1, , 360, 720, - 360 , 0 . : cos x = , ? , , .
4.1.2. ,
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4.1.3.ϳ
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, - 1 1). : cos x = 1/2. ? (³: 
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, : arccos 
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4.2.
4.2.1. , , ,
cos x = , ǀ a ǀ ≤ 1,
cos x = , ǀ a ǀ ≤ 1. ǀ a ǀ ≤ 1? , - . , 
- . , ? 
.
:
' : .
: 1) cos x = ,
2) ǀ a ǀ ≤ 1.
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4.2.2.
,
cos x = , ǀ a ǀ ≤ 1,
1. .
2. ³ , .
3. ³ , ( ).
4. .
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.( 1, , ǀ a ǀ ≤ 1) - , , : 
( ). 
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4.3.
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cos x = ? ?
1. ' , , .
2. cos x =3? ?
3. ` cos x = -1,5? cos x = 0?
, , ' .
: , cos x = , ǀ a ǀ ≤ 1.
: cos x = ǀ a ǀ >1, .
: , cos x = , ǀ a ǀ >1.
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IV.
1. ' :
sin 4x = 0;
cosx/5 = 1;
tgx+4 = 0;
sin(p/2-x) = -1;
cos(p/2+x) = 1;
3cos2x-7 = 0;
sin2x = ½;
V.
:
) (cos2x/2-sin2 x/2)2 - sin2x = -1/2;
cos2x-sin2x = -1/2;
cos2x = -1/2;
2x = + arcos(-1/2) + 2pn, n Z;
2x = + (-p/3) + 2 pn, n Z;
x = + (-2p/3) + 4pn, n Z;
) cosx - sinx = 2;
cosp/6cosx-sinp/6sinx = 1;
cos(p/6-x) = 1;
p/6-x = 2pn, n Z;
-x = 2pn-p/6;
x = p/6-2pn, n Z.
) 2sin2x-5sinx+2 = 0.
sinx = t;
2 t2-5 t+2 = 0;
D = 25-4*2*2+9;
t1 = 5+3/4 = 2;
t2 = 5-3/4 = ½;
sin x = 2;
x(-1) arcsin2 + pn, n Z;
x + (-1) p/6 + pn.
ϳ ' , , ' , ' .
, , ' 59 (26).
sin2x + sin(x-p/4) = 1.
VI. ϳ
³ , .
:
1. arcsin(-0,5):
) p/3;
) -p/6;
) -p/4;
) p/2?
2. :
) y = sinx;
) y = cosx;
) y = tgx.
3. y=arcos x :
) ;
) ;
) , .
4. y=arcos x:
) ;
) (-1; 1);
) (-p/2; p/2)?
5. arcsin 1:
) p/4;
) p/3;
) p/2;
) p;
) p/6.
6. y=arcsin x:
) R;
) (0; p);
) (-p/2; p/2);
) (-1; 1)?
7. y=arcsin x:
) ;
|
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) ;
) ;
) , ?
VII.
ϳ .
1. ' :
) ctg(x=p/3) = 1;
) 1-cosx = 4sin2x;
) sin2x-sin2x = 0.
2. ' :
sinx*siny + cosx*cosy = 1;
sinx*cosy + cosx*siny = ½.
