m
（Ⅱ）∵
∴
为锐角，
．
∴，
∴． -----------13分
2229.解: (Ⅰ)f?x?=?sin?x+cos?x?+2cos?x
=sin2?x+cos2?x+sin2?x+1+cos2?x
?sin2?x?cos2?x?2?2sin(2?x?)?2
42?2?3依题意得,故?的值为. ?22?3????5?(Ⅱ)因为-?x?,所以-?3x+?,
63444????-1?2sin?3x+??2
4???1?f?x??2+2,即f?x?的值域为??1,2+2? 9分
(Ⅲ)依题意得: g(x)?由2k?????5??2sin?3(x?)???2?2sin(3x?)?2
24?4?
5??≤2k??(k?Z)
2422?27?解得k??≤x≤k??(k?Z)
343122?27?故y?g(x)的单调增区间为: [k??,k??](k?Z)
34312≤3x?30. 【解析】解:(Ⅰ) 由p∥q得1?cos2A?3sinA,所以2sin2A?3sinA
又A为锐角∴sinA?而a2?13,
cosA?
22?c?b22222b?c?am
?mbc可以变形为?2bc2
m
即cosA?m?1,所以m?1
22
222(Ⅱ)由(Ⅰ)知 cosA?1,sinA?3 又b?c?a?1
222bc2所以bc?b2?c2?a22?2bc?a2即bc?a2
故S?ABC?1bcsinA?1a22333 ?244当且仅当b?c?3时,?ABC面积的最大值是33 31.解:(I)f(x)?cosxcos??sinxsin??cosx?1
232313??cosx?sinx?cosx?12213 ?cosx?sinx?1225??sin(x?)?16因此f(x)的值域为[0,2] (II)由f(B)?1得sin(B?又因0?B??,故B?25?5?)?1?1,即sin(B?)?0, 66?6.
222解法一:由余弦定理b?a?c?2accosB,得a?3a?2?0,解得a?1或2.
解法二:由正弦定理当C?3?2?bc,C?或得sinC? ?233sinBsinC,从而a??322??当C??时,A?,又B?,从而a?b?1.
366故a的值为1或2. 32.解:
(1)f(x)?a?b?a?2?所以,最小正周期为T?时,A??b2?c2?2;
??31???sin2x?cos2x?sin?2x?? 226??2??? 22k???2?2x??6?2k???2
所以,单调减区间为[2k???6,2k???3],(k?Z)
m
(2)f(A)?sin?2A????????5???????1,?A??0,?,2A????,?, 6?6?66??2?,
2?2A?2?62??2,A??3由a?b?c?2bccosA得b?4b?4?0,解得b?2 故S?21bcsinA?23 233.解：（Ⅰ）由sinx?0得x?kπ(k?Z)，
故f(x)的定义域为{x?R|x?kπ,k?Z}．…………………2分
(23sin2x?sin2x)?cosx因为f(x)??1
sinx?(23sinx?2cosx)?cosx?1 ?3sin2x?cos2x
π?2sin(2x?)，………………………………6分
6所以f(x)的最小正周期T?（II）由 x挝[,],2x当2x?当2x?2π?π．…………………7分 2??42???5?[,?],2x- [,],…………..9分 2636?5???,即x?时,f(x)取得最小值1，…………….11分 662????,即x?时,f(x)取得最大值2.……………….13分 623
m
34.
35.
13f(x)?2cosx(sinx?cosc)?3sin2x?sinxcosx2236.
m ?sinxcosx?3cos2x?3sin2x?sincosx?sin2x?3cos2x?2sin(2x?由 ?3)?3?2k???,k?Z232?7得k???x?k???,k?Z1212?2k??2x?? 7?],k?Z.12故函数f(x)的单调递减区间为[k???12,k??y?2sin(2x?（2）?y?2sin(2x??2??3?(m,0))?a????y?2sin(2x??3?2m) ?3?2m)的图象关于直线x??2对称.(k?Z)321??m??(k?1)??(k?Z)2125当k?0时,m的最小正值为?.1225????2m?k??? 37.解:(1)由题知(cos??cos?)2?(sin??sin?)2?25?2?2cos(???)?4,所以cos(???)?3 55(2)?0????,?????0 ?0??????，又cos(???)?3?sin(???)?4. 2255而cos(5???)??5则sin???5?cos??12?sin??sin[(???)??]?33 13213651338. （1）f(x)=sinxcos
7?7?3?3?+cosxsin+cosxcos+sinxsin
4444
1分
1分
=
2222sinx-cosx-cosx+sinx
2222
1分
=2sinx-2cosx =2sin(x-
?) 4
1分
∴T=2?
1分 1分
fmin（x）=-2
1?cos(2??)?222-2=-2sin? 2分 （2）[f（?）] -2=4sin（?-）-2=4·42Sin2?=sin[（?+?）+（?-?）] cos2?=-
1分
?449×-=-1
5525