高考三角函數(shù)大題全面分析

1、1 設(shè)銳角的內(nèi)角的對邊分別為,.()求的大小;()求的取值范圍.2 在中,角a bc的對邊分別為a、b、c,且滿足(2a-c)cosb=bcos c()求角b的大小; ()設(shè)且的最大值是5,求k的值.3 在中,角所對的邊分別為,.i.試判斷的形狀; ii.若的周長為16,求面積的最大值.4 在中,a、b、c分別是角a bc的對邊,c=2a,(1)求的值;(2)若,求邊ac的長5 已知在中,且與是方程的兩個根.()求的值;()若ab,求bc的長.6 在中,已知內(nèi)角a bc所對的邊分別為a、b、c,向量,且(i)求銳角b的大小;(ii)如果,求的面積的最大值7 在中,角a bc所對的邊分別是a,b

2、,c,且(1)求的值;(2)若b=2,求abc面積的最大值.8已知向量,與為共線向量,且()求的值;()求的值.9已知,求下列各式的值;(1);(2)10已知函數(shù)，求：（1）函數(shù)的定義域和值域； （2）寫出函數(shù)的單調(diào)遞增區(qū)間。11設(shè)函數(shù)（1）求函數(shù)上的單調(diào)遞增區(qū)間；（2）當(dāng)?shù)娜≈捣秶?2已知函數(shù)，（1）求的最大值和最小值；（2）在上恒成立，求實數(shù)的取值范圍13已知函數(shù).()求函數(shù)的最小正周期;()當(dāng)時,求函數(shù)的最大值,并寫出x相應(yīng)的取值.1.【解析】:()由,根據(jù)正弦定理得,所以,由為銳角三角形得.().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時,取最大值.依題意得,-2+4k+1=5,k=.3.【解析】:i.,所以此三角形為直角三角形.ii.,當(dāng)且僅當(dāng)時取等號,此時面積的最大值為.4.【解析】:(1)(2) 又 由解得a=4,c=6,即ac邊的長為5.5.【解析】:()由所給條件,方程的兩根. (),.由()知,為三角形的內(nèi)角, ,為三角形的內(nèi)角, 由正弦定理得: .6.【解析】:(1) 2sinb(2cos2-1)=-cos2b2sinbcosb=

4、-cos2b tan2b=-02b,2b=,銳角b=(2)由tan2b=- b=或當(dāng)b=時,已知b=2,由余弦定理,得:4=a2+c2-ac2ac-ac=ac(當(dāng)且僅當(dāng)a=c=2時等號成立)abc的面積sabc= acsinb=acabc的面積最大值為當(dāng)b=時,已知b=2,由余弦定理,得:4=a2+c2+ac2ac+ac=(2+)ac(當(dāng)且僅當(dāng)a=c=-時等號成立)ac4(2-)abc的面積sabc= acsinb=ac 2-abc的面積最大值為2-7.【解析】:(1) 由余弦定理:cosb= +cos2b= 待添加的隱藏文字內(nèi)容1(2)由 b=2, +=ac+42ac,得ac, sabc=a

5、csinb(a=c時取等號)故sabc的最大值為8.【解析】:() 與為共線向量, ,即 () , , 又, 因此, 9.【解析】: (1) (2) 10.【解析】: （）函數(shù)的定義域 函數(shù)的值域為 （）令得函數(shù)的單調(diào)遞增區(qū)間是 11.【解析】：（1）， （2）當(dāng)，12.【解析】（） 又，即，（），且，即的取值范圍是13.解析:()因為 ( ) 所以,即函數(shù)的最小正周期為 ()因為,得,所以有 ,即 所以,函數(shù)的最大值為 此時,因為,所以,即 c29c91afe4ced1b6c8795ad9c91afe4ced1b6c8795ad91afe4ced1b6c8795ad9c91fe4ced1b6

6、c8795ad29c91afedd1b6c87d1b6c8795ad9c91afe4ced1b6c8795ad91afe4ced1b6c8795ad9c91fe4ced1b6c8795ad29c91af95ad9c91afe4ced1b6c8795ad91afe4ced1b6c8795ad9d1b6c8795ad9c91afe4ced1b6c8795a1afe4ced1b6c8795ad91afe4ced1b6c8795ad9c91fe4ced1b6c8795ad29c91afc91fe4ced1d1b6c8795ad9c91afe4ced1b6c8795ad91afe4ced1b6cd1b6

7、c8795ad9c91afe4ced1b6c8795ad91afe4ced1b6c8795ad9c91fe4ced1b6c8795ad29c91af8795ad9c91fe4ced1d1b6c8795ad9c91afe4ced1b6c8795ad91afe4ced1b6c87d1b6c8795ad9c91afe4ced1b6c8795ad91afe4ced1b6c8795ad9c91fe4ced1b6c8795ad29c91af5d1b6c8795ad9c91afe4ced1b6c8795ad91afe4ced1b6c8795ad9c91fe4ced1b6c8795ad29c91afad9c9

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