a) -2cos = 1; ) cos 2 - 1 = 0;
) 2cos = ; ) - 2cos = 0.
: ) +2πn, n Z; ) π n, n Z;
) +π n, n Z; r) + , n Z.
: : ,
, , : , x = π + 2π, Z, ; ) , x = + 2π, Z, .
4.2. ' sin x = a.
1. | | > 1, ', | sin x | 1 - x.
2. | | < 1, , , sin x x , : , , ( OY , (. 123), - ):
x 1 = arcsin a + 2π, Z,
x 2 = π - arcsin + 2π, Z.
ֳ :
x = (-1) k arcsin a + πk, k Z | (1) |
, k = 2 :
x 1 = (-1)2 n arcsin + 2π x 1 = arcsin a + 2π, Z;
k = 2 n + 1 :
x 2 = (-1)2 n +1 arcsin + (2 n + 1)π;
x 2 = - arcsin + 2π + π;
x 2 = π - arcsin a + 2π, Z.
.
= 1, , , sin t Pt( , : , 1, t 0(1;0) + 2π, Z.
, t = + 2π, Z.
= -1, t = - + 2π, Z. "
= 0, t = 0 + π ; t =π, Z.
.
1. ' sinx = .
'
(1) : = (-1) n arcsin + π , Z.
arcsin = , = (-1) n + π n, Z.
: (-1) n + π n, Z.
2. ' sin = - .
'
(1) : = (-1) n arcsin + π , Z.
arcsin = - , = (-1) n + π n, n Z; = (-1) n +1 + π , Z.
: (-1) n +1 + π , Z.
3. ' sin x = .
'
, (1) : = (-1) n arcsin + π , Z.
: (-1) n arcsin + π , Z.
( , , )
a) 2sin - 1 = 0; ) 2sin = - l;
) 2sin = - ; ) 2sin = .
: ) (-1) n + π n, n Z; ) (-1) n+ 1 + 2π, Z;
) +(-1) n +1 + , Z; ) +(-l) n +1 +4π n, Z
4.4. ' tg x = a (ctg x = a).
|
|
' tg x = (. 1). tg x x . ³ , , ,
x = arctg + π n, n Z | (1) |
, tg x = - '.
г ctg x = , ≠ 0 tg x = .
, ' ctg x = : x = arcctg a + π , n Z
.
1. ' tg x = .
'
(1) = arctg + π , Z.
arctg = , : = + π , Z.
: + π , Z.
2. ' tg = 2.
'
(1) : = arctg 2 + π , Z.
: arctg 2 + π 1,1 + π , Z.
3. ' ctg x = 0.
'
ctg = 0; ctg = ; tg = , x = arctg + π = + π n, n Z.
: + π n, n Z.
5. , . (, )
, :
1. . (cosx = , sinx = , tgx = ctgx = ).
2. , .
3. .
6.ϳ .()
:
1. ?
2. ?
3. ?
4. ?
, , .
7. . .