# Решение однородных тригонометрических уравнений 1. , ? 1) arc tg 1 2) arc tg (- 3 ) 3) arc tg 0 4) tg (arc cos ) 5) tg (arc ctg 3 ) 1 3 1

2 4 - 3 6 5 3 4

0 2 3 2. 1) cos x = , 2) sin = 3 /2, 1 3) tg x =/4, 4) os x = 3/2, 5) sin x = 1/3, 6) cos x = - 3 / 2,

1/2 7) cos x = /3, /3 =/6 +2/6 +2n (-1)n =/3 +n /4 =1+n 2n =/6 +2/6 + n n =(-1)n arcsin 1/3 + 2n 5/6 =/6 +2/6 +2n /3 =/6 +21/2 +2n.

; ; ; ; ; . 1) 3tg2x1 tg2x 1 3 2x arctg1 n,n,nZ 3 n,

2x n,n,n Z 6 x n, n,n,nZ 12 2 3. 1. 2sinx 7sinx + 3 = 0 1. 2sinx 7sinx + 3 = 0 2. 3sinx cos4x cos4x = 0 sinx = t , : 2t 7t + 3 = 0 3. 2 sinx -3 cosx = 0 4. 3 sinx-4 sinx cosx+cosx = 0 2. 3sinx cos4x cos4x =0 cos4x (3sinx 1) = 0 cos4x =0 3sin x-1=0

3. 2 sinx -3 cosx = 0 4. 3 sinx-4 sinx cosx+cosx = 0 . . asinx + bcosx =0, 0, b0 asin x + bsinx cosx + ccos x =0 , 0, b0, 0 . . :

1) sin x = 2 cos x ; 2) 2 sin x + 3cos x = 0 ; 3) 3 sin x + 5 cos x = 0 ; 4) 2 sin x + cos x = 2 ; 5) sinx - 2 sinx cosx + 4 cosx = 0 . : 1) 3 sinx cosx 0; 2) sinx 2 2 x 10sinx cosx 21cos 3) sin 2x 6sin2x os2xos2x 5cos 2 2

1. 2. x 0; 2x 0; 2 4) 6sin x 4sin( - x ) cos( 2 - x ) 1. = -/6 +n =1/2 arctg5+/2 n =/8+/2 n 3

. 1603) =arctg7+ n =arctg3+ n = arctg(1/5)+ n =- /4 +n (1540- 4. 1

2 3 sin3x - cos3x = 0 5 sinx +6 cosx = 0 4 Sinx - 5 sinx cosx + 4cosx = 0 sinx - 4 sinx cosx - 5cosx = 0 5 3sinx sinx cosx = 2 4sinx+2sin x cosx = 3

: 7.17. 2 1 .