) )
) cos x = p/4 , . cos x
- :
) - ,
: 3cos x + 4 0; cos x -4/3, , 0.
: nÎ Z
) a 0, 0, 0:
2 sin2 x 3 sin x = 0
1 + cos x 0
: 2 sin2x 3sinx = 0; sinx(2 sinx - 3) = 0,
sinx = 0 2 sinx 3 = 0
1) sinx = 0, = pn, nÎ Z;
2) 2 sinx 3 = 0; sinx = -
: 1 + cos x 0 , cos x -1, .. x p + 2pk, kÎZ
, :
= pn, nÎ Z;
x p +2pk, kÎ Z
:
= pn, nÎZ , p 0 0 2p
x p + 2pk, kÎ Z.
: = 2pn, nÎZ ( 2pn, 4pn)
: = 2pn, nÎ Z
:
) ; ;
:
;
: ,
) cos (p/4 + x) tg 3x cos (p/4 + x) = 0;
cos (p/4 + x), cos (p/4 + x)(1 - tg 3x) = 0,
cos (p/4 + x) = 0 ( )
1 - tg 3x = 0
p/4 + x = p/2 + pn
tg 3x = 1 ( )
x = p/2 - p/4 + pn
3x = p/4 + pn
x = p/4 + pn
x = p/12 + pn/3 :{ p/4 + pn; p/12 + pn/3, nÎ Z}
( ):
-
: nÎ Z
:
:
(1) - 1 ()
(2) - II .
(1) , , b ,
cos x , .
cos x, :
tg + b=0, ; -
, 1 nÎ Z
:
sinx + cosx = 0; x = - arcctg ; x = - arcctg +pn; x = - -
(2)
;
cos2x : ,
: :
, , tgx, .
:
,
;
- ;
,
:
nÎZ
.
, ( ).
|
|
) sin x cos y = 1 (1)
sin x + cos y = 0 (2) (1) (2),
2 sin x = 1 sin x =1/2 x =(-1)k p/6 + pk, kÎZ
2 cos y = -1 cos y = -1/2 x = 2p/3 + 2pn, nÎZ
: x =(-1)k p/6 + pk, kÎZ
x = 2p/3 + 2pn, nÎZ
) x + y = p
cos x cos y = 1 = p - , cos x cos (p - ) = 1; cos x + cos x =1; 2 cos x = 1; cos x = ½;
x = p/3 + 2pn, nÎZ
= p - ( p/3 + 2pn) = p/3 + (1 2n)p, nÎZ
: x = p/3 + 2pn, = p/3 + (1 2n)p, nÎZ.