1、 - 1 - 04 1 f(x)=2cosxsin(x+ /3)- 3sin 2 x+snxcosx (1) f(x) ; (2) f(x) m x= /2 , m . 2 A(cos ,sin ),B(cos ,sin ), 5|AB|=2, (1) cos( - ) ; (2) (0, /2), (- /2,0), cos(5 /2- )=-5/13, sin . 3 f x =sin 4 7 x +cos 4 3 x x 12 1 f x 6 2 cos - = 5 4 cos + = - 5 4 ,0b=1 1 a= 2 1 C= 4 3 1 - 6 - c 2 =a 2 +b
2、 2 -2abcosC=5 c= 5 5. (I): 1 cos 2 3(1 cos 2 ) ( ) 3 sin 2 22 xx f x x 2 3sin 2 cos 2 xx 2sin(2 ) 2 6 x 2 2 T , 2 2 2 , 2 6 2 k x k k Z () fx () fx , , 36 k k k Z (II) : ( ) 2 2sin(2 ) 6 f x x , : 63 x 5 2 , 6 6 6 x , 1 sin(2 ) ,1 62 x ( ) 1, 4 fx () fx 1,4 6. :(1) | | 2 AB AC AB AC | | 2 AB AC BC a
3、 2 2 2 2 cos cos 2 b c a bc A bc A 2 2 2 2 | | | | 8 AB AC b c (2) 1 sin 2 ABC S bc A = 2 1 1 cos 2 bc A - 7 - = 2 12 1 ( ) 2 bc bc = 2 1 ( ) 4 2 bc 22 2 1 ( ) 4 22 bc = 3 b=c=2 A= 3 7. (1) 2 1 ) 6 2 sin( ) ( x x f , T (2) 2 3 , 2 3 18. f(x) 3sin2x cos2x 2sin(2x 6 ) (1) 2k 2 2x 6 2k 3 2 (k Z) k 6
4、x k 2 3 (k Z) f(x) k 6 k 2 3 (k Z) (2) sin(2x 6 ) 0 2x 6 k(k Z) x k 2 12 (k Z) f(x) ( 12 0) 9. 1 x x x x x x f 2 cos 2 cos 2 1 2 sin 2 3 1 cos 2 ) 6 2 sin( ) ( 2 ) 6 2 sin( 2 cos 2 1 2 sin 2 3 x x x - 8 - ) ( 2 2 6 2 2 2 Z k k x k ) (x f ) ( 6 , 3 Z k k k 2 2 1 ) ( A f 2 1 ) 6 2 sin( A 6 2 6 2 6 A 6 5 6 2 A 3 A b,a,c 2a=b+c 9 AC AB 9 cos A bc 18 bc bc c b A bc c b a 3 ) ( cos 2 2 2 2 2 18 3 4 2 2 a a 2 3 a
