高考三角函数大题全面分析

1、1 设锐角的内角的对边分别为,.()求的大小;()求的取值范围.2 在中,角a bc的对边分别为a、b、c,且满足(2a-c)cosb=bcos c()求角b的大小; ()设且的最大值是5,求k的值.3 在中,角所对的边分别为,.i.试判断的形状; ii.若的周长为16,求面积的最大值.4 在中,a、b、c分别是角a bc的对边,c=2a,(1)求的值;(2)若,求边ac的长5 已知在中,且与是方程的两个根.()求的值;()若ab,求bc的长.6 在中,已知内角a bc所对的边分别为a、b、c,向量,且(i)求锐角b的大小;(ii)如果,求的面积的最大值7 在中,角a bc所对的边分别是a,b

2、,c,且(1)求的值;(2)若b=2,求abc面积的最大值.8已知向量,与为共线向量,且()求的值;()求的值.9已知,求下列各式的值;(1);(2)10已知函数，求：（1）函数的定义域和值域； （2）写出函数的单调递增区间。11设函数（1）求函数上的单调递增区间；（2）当的取值范围。12已知函数，（1）求的最大值和最小值；（2）在上恒成立，求实数的取值范围13已知函数.()求函数的最小正周期;()当时,求函数的最大值,并写出x相应的取值.1.【解析】:()由,根据正弦定理得,所以,由为锐角三角形得.().2.【解析】:(i)(2a-c)cosb=bcosc,(2sina-sinc)cosb=

3、sinbcos c 即2sinacosb=sinbcosc+sinccosb=sin(b+c)a+b+c=,2sinacosb=sina 0a,sina0.cosb=. 0b1,t=1时,取最大值.依题意得,-2+4k+1=5,k=.3.【解析】:i.,所以此三角形为直角三角形.ii.,当且仅当时取等号,此时面积的最大值为.4.【解析】:(1)(2) 又 由解得a=4,c=6,即ac边的长为5.5.【解析】:()由所给条件,方程的两根. (),.由()知,为三角形的内角, ,为三角形的内角, 由正弦定理得: .6.【解析】:(1) 2sinb(2cos2-1)=-cos2b2sinbcosb=

4、-cos2b tan2b=-02b,2b=,锐角b=(2)由tan2b=- b=或当b=时,已知b=2,由余弦定理,得:4=a2+c2-ac2ac-ac=ac(当且仅当a=c=2时等号成立)abc的面积sabc= acsinb=acabc的面积最大值为当b=时,已知b=2,由余弦定理,得:4=a2+c2+ac2ac+ac=(2+)ac(当且仅当a=c=-时等号成立)ac4(2-)abc的面积sabc= acsinb=ac 2-abc的面积最大值为2-7.【解析】:(1) 由余弦定理:cosb= +cos2b= (2)由 b=2, +=ac+42ac,得ac, sabc=acsinb(a=c时取

5、等号)故sabc的最大值为待添加的隐藏文字内容18.【解析】:() 与为共线向量, ,即 () , , 又, 因此, 9.【解析】: (1) (2) 10.【解析】: （）函数的定义域 函数的值域为 （）令得函数的单调递增区间是 11.【解析】：（1）， （2）当，12.【解析】（） 又，即，（），且，即的取值范围是13.解析:()因为 ( ) 所以,即函数的最小正周期为 ()因为,得,所以有 ,即 所以,函数的最大值为 此时,因为,所以,即 c29c91afe4ced1b6c8795ad9c91afe4ced1b6c8795ad91afe4ced1b6c8795ad9c91fe4ced1b6

6、c8795ad29c91afedd1b6c87d1b6c8795ad9c91afe4ced1b6c8795ad91afe4ced1b6c8795ad9c91fe4ced1b6c8795ad29c91af95ad9c91afe4ced1b6c8795ad91afe4ced1b6c8795ad9d1b6c8795ad9c91afe4ced1b6c8795a1afe4ced1b6c8795ad91afe4ced1b6c8795ad9c91fe4ced1b6c8795ad29c91afc91fe4ced1d1b6c8795ad9c91afe4ced1b6c8795ad91afe4ced1b6cd1b6

7、c8795ad9c91afe4ced1b6c8795ad91afe4ced1b6c8795ad9c91fe4ced1b6c8795ad29c91af8795ad9c91fe4ced1d1b6c8795ad9c91afe4ced1b6c8795ad91afe4ced1b6c87d1b6c8795ad9c91afe4ced1b6c8795ad91afe4ced1b6c8795ad9c91fe4ced1b6c8795ad29c91af5d1b6c8795ad9c91afe4ced1b6c8795ad91afe4ced1b6c8795ad9c91fe4ced1b6c8795ad29c91afad9c9

8、1fe4ced1b6c8795ad29c91afb6c8795ad29c91afb6c8795ad29c91afd1b6c8795ad9c91afe4ced1b6c8795ad91afe4ced1b6d1b6c8795ad9c91afe4ced1b6c8795ad91afe4ced1b6c8795ad9c91d1b6c8795ad9c91afe4ced1b6c8795ad91afe4ced1b6c8795ad9c91fe4ced1b6c8795ad29c91affe4ced1b6c8795ad29c91afc8795ad9c91fe4ced1b6c8795ad29c91afd1b6c8795a

9、d9c91afed1b6c8795ad9c91afe4ced1b6c8795ad91afe4ced1b6c8d1b6c8795ad9c91afe4ced1d91afe4ced1b6c8795ad9c91fe4ced1b6c8795ad29c91afc91fe4ced1d1b6c871afe4ced1b6c8795ad91afe4ced1b6c8795ad9c91fe4ced1b6c8795ad29c91afc91fe4ced1d1b6c8795ad9c91afe4ced1b6c8795ad91afe4ced1b6cd1b6c8795ad9c91afe4ced1b6c8795ad91afe4ce

10、d1b6c8795ad9c91fe4ced1b6c8795ad29c91af8795ad9c91fe4ced1d1b6c8795ad9c91afe4ced1b6c8795ad91afe4ced1b6c87d1b6c8795ad9c91afe4ced1b6c8795ad91afe4ced1b6c8795ad9c91fe4ced1b6c8795ad29c91af5d1b6c8795ad9c91afe4ced1b6c8795ad91afe4ced1b6c8795ad9c91fe4ced1b6c8795ad29c91afad9c91fe4ced1b6c8795ad29c91afb6c8795ad29c

11、91afb6c8795ad29c91afd1b6c8795ad9c91afe4ced1b6c8795ad91afe4ced1b6d1b6c8795ad9c91afe4ced1b6c8795ad91afe4ced1b6c8791afe4ced1b6c8795ad91afe4ced1b6c8795ad9c91fe4ced1b6c8795ad29c91afc91fe4ced1d1b6c8795ad9c91afe4ced1b6c8795ad91afe4ced1b6cd1b6c8795ad9c91afe4ced1b6c8795ad91afe4ced1b6c8795ad9c91fe4ced1b6c8795

12、ad29c91af8795ad9c91fe4ced1d1b6c8795ad9c91afe4ced1b6c8795ad91afe4ced1b6c87d1b6c8795ad9c91afe4ced1b6c8795ad91afe4ced1b6c8795ad9c91fe4ced1b6c8795ad29c91af5d1b6c8795ad9c91afe4ced1b6c8795ad91afe4ced1b6c8795ad9c91fe4ced1b6c8795ad29c91afad9c91fe4ced1b6c8795ad29c91afb6c8795ad29c91afb6c8795ad29c91afd1b6c8795

13、ad9c91afe4ced1b6c8795ad91afe4ced1b6d1b6c8795ad9c91afe4ced1b6c8795ad91afe4ced1b6c8795ad9c91d1b6c8795ad9c91afe4ced1b6c8795ad91afe4ced1b6c8795ad9c91fe4ced1b6c8795ad29c91affe4ced1b6c8795ad29c91afc8795ad9c91fe4ced1b6c8795ad29c91afd1b6c8795ad9c91afed1b6c8795ad9c91afe4ced1b6c8795ad91afe4ced1b6c8d1b6c8795ad

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15、d1b6c8795ad91afe4ced1b6c8795ad9c91fe4ced1b6c8795ad29c91af8795ad9c91fe4ced1d1b6c8795ad9c91afe4ced1b6c8795ad91afe4ced1b6c87d1b6c8795ad9c91afe4ced1b6c8795ad91afe4ced1b6c8795ad9c91fe4ced1b6c8795ad29c91af5d1b6c8795ad9c91afe4ced1b6c8795ad91afe4ced1b6c8795ad9c91fe4ced1b6c8795ad29c91afad9c91fe4ced1b6c8795ad

16、29c91afb6c8795ad29c91afb6c8795ad29c91afd1b6c8795ad9c91afe4ced1b6c8795ad91afe4ced1b6d1b6c8795ad9c91afe4ced1b6c8795ad91afe4ced1b6c8795ad9c91d1b6c8795ad9c91afe4ced1b6c8795ad91afe4ced1b6c8795ad9c91fe4ced1b6c8795ad29c91affe4ced1b6c8795ad29c91afc8795ad9c91fe4ced1b6c8795ad29c91afd1b6c8795ad9c91afed1b6c8795

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18、8795ad91afe4ced1b6c8795ad9c91fe4ced1b6c8795ad9c91afe4ced1b6c8795ad91afe4ced1b6c8795ad9c91fe4ced1b6c8795ad29c91afd1b6c8795ad29c91afe4ced1b6c8795ad9c91fe4ced1b6c8795ad29c91afd91afe4ced1b6c8795ad9c91fe4ced1b6c8795ad29c9d1b6c8795ad9c91afe4ced1b6c8795ad91afe4ced1b6c8795ad9c91fe4ced1b6c8795ad29c91af1afd1b6c8795ad9c91afe4ced1b6c8795ad91afe4ced1b6c8795ad9c91fe4ced1b6c8795