新高考數(shù)學(xué)二輪復(fù)習(xí)分層訓(xùn)練專題08 三角函數(shù)圖像與性質(zhì)(原卷版)_第1頁
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答案第=page11頁,共=sectionpages22頁專題08三角函數(shù)圖像與性質(zhì)【練基礎(chǔ)】一、單選題1.(2023·云南昆明·昆明一中校考模擬預(yù)測)函數(shù)SKIPIF1<0的最大值為(

)A.1 B.3 C.5 D.SKIPIF1<02.(2023·陜西·西安市西光中學(xué)校聯(lián)考一模)函數(shù)SKIPIF1<0在SKIPIF1<0上有唯一的極大值,則SKIPIF1<0(

)A.SKIPIF1<0 B.SKIPIF1<0 C.SKIPIF1<0 D.SKIPIF1<03.(2023·內(nèi)蒙古赤峰·統(tǒng)考模擬預(yù)測)已知函數(shù)SKIPIF1<0,則下列結(jié)論不正確的是(

)A.SKIPIF1<0的圖像與直線SKIPIF1<0的兩個(gè)相鄰交點(diǎn)的距離為SKIPIF1<0B.SKIPIF1<0C.將SKIPIF1<0的圖像向右平移SKIPIF1<0個(gè)單位得到的圖像關(guān)于y軸對(duì)稱D.SKIPIF1<0在區(qū)間SKIPIF1<0上單調(diào)遞減,則a的最大值為SKIPIF1<04.(2023·山西·統(tǒng)考一模)定義在SKIPIF1<0上的函數(shù)SKIPIF1<0滿足在區(qū)間SKIPIF1<0內(nèi)恰有兩個(gè)零點(diǎn)和一個(gè)極值點(diǎn),則下列說法正確的是(

)A.SKIPIF1<0的最小正周期為SKIPIF1<0B.將SKIPIF1<0的圖象向右平移SKIPIF1<0個(gè)單位長度后關(guān)于原點(diǎn)對(duì)稱C.SKIPIF1<0圖象的一個(gè)對(duì)稱中心為SKIPIF1<0D.SKIPIF1<0在區(qū)間SKIPIF1<0上單調(diào)遞增5.(2023·陜西·西安市西光中學(xué)校聯(lián)考一模)函數(shù)SKIPIF1<0在SKIPIF1<0上恰有兩個(gè)極大值點(diǎn),則SKIPIF1<0(

)A.SKIPIF1<0 B.SKIPIF1<0 C.SKIPIF1<0 D.SKIPIF1<06.(2023·福建·統(tǒng)考一模)函數(shù)SKIPIF1<0恒有SKIPIF1<0,且SKIPIF1<0在SKIPIF1<0上單調(diào)遞增,則SKIPIF1<0的值為(

)A.SKIPIF1<0 B.SKIPIF1<0 C.SKIPIF1<0 D.SKIPIF1<0或SKIPIF1<07.(2023·安徽馬鞍山·統(tǒng)考一模)已知函數(shù)SKIPIF1<0(SKIPIF1<0,SKIPIF1<0)的圖象經(jīng)過點(diǎn)SKIPIF1<0,若函數(shù)SKIPIF1<0在區(qū)間SKIPIF1<0內(nèi)恰有兩個(gè)零點(diǎn),則實(shí)數(shù)SKIPIF1<0的取值范圍是(

)A.SKIPIF1<0 B.SKIPIF1<0C.SKIPIF1<0 D.SKIPIF1<08.(2023·廣西柳州·統(tǒng)考模擬預(yù)測)已知函數(shù)SKIPIF1<0,其圖象相鄰兩條對(duì)稱軸的距離為SKIPIF1<0,且對(duì)任意SKIPIF1<0,都有SKIPIF1<0,則在下列區(qū)間中,SKIPIF1<0為單調(diào)遞減函數(shù)的是(

)A.SKIPIF1<0 B.SKIPIF1<0 C.SKIPIF1<0 D.SKIPIF1<0二、多選題9.(2023·浙江·永嘉中學(xué)校聯(lián)考模擬預(yù)測)已知函數(shù)SKIPIF1<0,將函數(shù)SKIPIF1<0的圖象向右平移SKIPIF1<0個(gè)單位長度,再把橫坐標(biāo)縮小為原來的SKIPIF1<0(縱坐標(biāo)不變),得到函數(shù)SKIPIF1<0的圖象,則(

)A.SKIPIF1<0的周期為SKIPIF1<0B.SKIPIF1<0為奇函數(shù)C.SKIPIF1<0的圖象關(guān)于點(diǎn)SKIPIF1<0對(duì)稱D.當(dāng)SKIPIF1<0時(shí),SKIPIF1<0的取值范圍為SKIPIF1<010.(2023·遼寧·遼寧實(shí)驗(yàn)中學(xué)??寄M預(yù)測)已知函數(shù)SKIPIF1<0(其中ω>0,0<φ<π)的圖像與x軸相鄰兩個(gè)交點(diǎn)之間的最小距離為SKIPIF1<0,當(dāng)SKIPIF1<0時(shí),f(x)的圖像與x軸的所有交點(diǎn)的橫坐標(biāo)之和為SKIPIF1<0,則(

)A.SKIPIF1<0B.f(x)在區(qū)間SKIPIF1<0內(nèi)單調(diào)遞增C.f(x)的圖像關(guān)于點(diǎn)SKIPIF1<0對(duì)稱D.f(x)的圖像關(guān)于直線SKIPIF1<0對(duì)稱11.(2023·重慶·統(tǒng)考一模)已知SKIPIF1<0(其中SKIPIF1<0,SKIPIF1<0)的部分圖像如圖所示,則下列說法正確的是(

)A.SKIPIF1<0B.SKIPIF1<0C.函數(shù)SKIPIF1<0在區(qū)間SKIPIF1<0單調(diào)遞減D.若SKIPIF1<0,且SKIPIF1<0,則SKIPIF1<012.(2023·湖北·校聯(lián)考模擬預(yù)測)已知函數(shù)SKIPIF1<0,則(

)A.SKIPIF1<0的圖象可由SKIPIF1<0的圖象向右平移SKIPIF1<0個(gè)單位長度得到B.SKIPIF1<0在SKIPIF1<0上單調(diào)遞增C.SKIPIF1<0在SKIPIF1<0內(nèi)有2個(gè)零點(diǎn)D.SKIPIF1<0在SKIPIF1<0上的最大值為SKIPIF1<0三、填空題13.(2023·遼寧·校聯(lián)考模擬預(yù)測)已知函數(shù)SKIPIF1<0(SKIPIF1<0,SKIPIF1<0)在區(qū)間SKIPIF1<0內(nèi)單調(diào),在區(qū)間SKIPIF1<0內(nèi)不單調(diào),則ω的值為______.14.(2023·湖南長沙·統(tǒng)考一模)已知函數(shù)SKIPIF1<0,若函數(shù)SKIPIF1<0的圖象關(guān)于點(diǎn)SKIPIF1<0中心對(duì)稱,且關(guān)于直線SKIPIF1<0軸對(duì)稱,則SKIPIF1<0的最小值為______.15.(2022·四川綿陽·四川省綿陽南山中學(xué)??级#┖瘮?shù)SKIPIF1<0的圖象如圖,則SKIPIF1<0的值為______.16.(2022·四川廣安·廣安二中校考模擬預(yù)測)已知曲線SKIPIF1<0相鄰對(duì)稱軸之間的距離為SKIPIF1<0,且函數(shù)SKIPIF1<0在SKIPIF1<0處取得最大值,則下列結(jié)論正確的序號(hào)是______.①當(dāng)SKIPIF1<0時(shí),SKIPIF1<0的取值范圍是SKIPIF1<0;②將SKIPIF1<0的圖象向左平移SKIPIF1<0個(gè)單位后所對(duì)應(yīng)的函數(shù)為偶函數(shù);③函數(shù)SKIPIF1<0的最小正周期為SKIPIF1<0;④函數(shù)SKIPIF1<0在區(qū)間SKIPIF1<0上有且僅有一個(gè)零點(diǎn).四、解答題17.(2023·北京順義·統(tǒng)考一模)已知函數(shù)SKIPIF1<0的一個(gè)零點(diǎn)為SKIPIF1<0.(1)求A和函數(shù)SKIPIF1<0的最小正周期;(2)當(dāng)SKIPIF1<0時(shí),若SKIPIF1<0恒成立,求實(shí)數(shù)m的取值范圍.18.(2023·廣東東莞·校考模擬預(yù)測)已知函數(shù)SKIPIF1<0.(1)求SKIPIF1<0的最小正周期及對(duì)稱軸方程;(2)SKIPIF1<0時(shí),SKIPIF1<0的最大值為SKIPIF1<0,最小值為SKIPIF1<0,求SKIPIF1<0,SKIPIF1<0的值.19.(2023·上海靜安·統(tǒng)考一模)平面向量SKIPIF1<0,函數(shù)SKIPIF1<0.(1)求函數(shù)y=SKIPIF1<0的最小正周期;(2)若SKIPIF1<0,求y=SKIPIF1<0的值域;(3)在△SKIPIF1<0中,內(nèi)角SKIPIF1<0的對(duì)邊分別為SKIPIF1<0,已知SKIPIF1<0,SKIPIF1<0,求△SKIPIF1<0的面積.20.(2022·重慶江北·??家荒#┮阎蛄縎KIPIF1<0,且SKIPIF1<0,(1)求函數(shù)SKIPIF1<0在SKIPIF1<0上的值域;(2)已知SKIPIF1<0的三個(gè)內(nèi)角分別為SKIPIF1<0,其對(duì)應(yīng)邊分別為SKIPIF1<0,若有SKIPIF1<0,SKIPIF1<0,求SKIPIF1<0面積的最大值.【提能力】一、單選題21.(2023·全國·校聯(lián)考模擬預(yù)測)已知函數(shù)SKIPIF1<0在區(qū)間SKIPIF1<0上單調(diào)遞增,則SKIPIF1<0的取值范圍是(

)A.SKIPIF1<0 B.SKIPIF1<0 C.SKIPIF1<0 D.SKIPIF1<022.(2023·全國·模擬預(yù)測)已知SKIPIF1<0.若存在SKIPIF1<0,使不等式SKIPIF1<0有解,則實(shí)數(shù)m的取值范圍為(

)A.SKIPIF1<0 B.SKIPIF1<0 C.SKIPIF1<0 D.SKIPIF1<023.(2023·四川涼山·統(tǒng)考一模)已知函數(shù)SKIPIF1<0,關(guān)于函數(shù)SKIPIF1<0有如下四個(gè)命題:①SKIPIF1<0的最小正周期是SKIPIF1<0;②若SKIPIF1<0在SKIPIF1<0處取得極值,則SKIPIF1<0;③把SKIPIF1<0的圖象向右平行移動(dòng)SKIPIF1<0個(gè)單位長度,所得的圖象關(guān)于坐標(biāo)原點(diǎn)對(duì)稱;④SKIPIF1<0在區(qū)間SKIPIF1<0上單調(diào)遞減,則SKIPIF1<0的最小值為SKIPIF1<0.其中真命題的個(gè)數(shù)為(

)A.1 B.2 C.3 D.424.(2023·全國·高三專題練習(xí))將函數(shù)SKIPIF1<0的圖象向左平移SKIPIF1<0個(gè)單位長度得到如圖所示的奇函數(shù)SKIPIF1<0的圖象,且SKIPIF1<0的圖象關(guān)于直線SKIPIF1<0對(duì)稱,則下列選項(xiàng)不正確的是(

)A.SKIPIF1<0在區(qū)間SKIPIF1<0上為增函數(shù) B.SKIPIF1<0C.SKIPIF1<0 D.SKIPIF1<025.(2023秋·廣西河池·高三統(tǒng)考期末)已知函數(shù)SKIPIF1<0,則下列說法正確的是(

)A.SKIPIF1<0的一條對(duì)稱軸為SKIPIF1<0B.SKIPIF1<0的一個(gè)對(duì)稱中心為SKIPIF1<0C.SKIPIF1<0在SKIPIF1<0上的值域?yàn)镾KIPIF1<0D.SKIPIF1<0的圖象可由SKIPIF1<0的圖象向右平移SKIPIF1<0個(gè)單位得到26.(2023·全國·高三專題練習(xí))已知函數(shù)SKIPIF1<0,SKIPIF1<0,且SKIPIF1<0在SKIPIF1<0上恰有50個(gè)零點(diǎn),則SKIPIF1<0的取值范圍是(

)A.SKIPIF1<0 B.SKIPIF1<0 C.SKIPIF1<0 D.SKIPIF1<027.(2022·四川遂寧·統(tǒng)考一模)函數(shù)SKIPIF1<0,SKIPIF1<0,滿足SKIPIF1<0,若SKIPIF1<0,在SKIPIF1<0有兩個(gè)實(shí)根,則m的取值范圍為(

)A.SKIPIF1<0 B.SKIPIF1<0 C.SKIPIF1<0 D.SKIPIF1<028.(2023秋·天津南開·高三崇化中學(xué)??计谀┮阎猄KIPIF1<0,函數(shù)SKIPIF1<0恰有3個(gè)零點(diǎn),則m的取值范圍是(

)A.SKIPIF1<0 B.SKIPIF1<0 C.SKIPIF1<0 D.SKIPIF1<0二、多選題29.(2023·廣東肇慶·統(tǒng)考二模)函數(shù)SKIPIF1<0的部分圖像如圖所示,SKIPIF1<0,則下列選項(xiàng)中正確的有(

)A.SKIPIF1<0的最小正周期為SKIPIF1<0B.SKIPIF1<0是奇函數(shù)C.SKIPIF1<0的單調(diào)遞增區(qū)間為SKIPIF1<0D.SKIPIF1<0,其中SKIPIF1<0為SKIPIF1<0的導(dǎo)函數(shù)30.(2023·安徽淮南·統(tǒng)考一模)已知函數(shù)SKIPIF1<0圖像過點(diǎn)SKIPIF1<0,且存在SKIPIF1<0,當(dāng)SKIPIF1<0時(shí),SKIPIF1<0,則(

)A.SKIPIF1<0的周期為SKIPIF1<0B.SKIPIF1<0圖像的一條對(duì)稱軸方程為SKIPIF1<0C.SKIPIF1<0在區(qū)間SKIPIF1<0上單調(diào)遞減D.SKIPIF1<0在區(qū)間SKIPIF1<0上有且僅有4個(gè)極大值點(diǎn)31.(2023·河北衡水·河北衡水中學(xué)??寄M預(yù)測)已知函數(shù)SKIPIF1<0,其中SKIPIF1<0、SKIPIF1<0.則下列說法中正確的有(

).A.SKIPIF1<0的最小值為SKIPIF1<0B.SKIPIF1<0的最大值為SKIPIF1<0C.方程SKIPIF1<0在SKIPIF1<0上有三個(gè)解D.SKIPIF1<0在SKIPIF1<0上單調(diào)遞減32.(2022·安徽黃山·統(tǒng)考一模)已知函數(shù)SKIPIF1<0,現(xiàn)將函數(shù)SKIPIF1<0的圖象沿x抽向左平移SKIPIF1<0單位后,得到一個(gè)偶函數(shù)的圖象,則(

)A.函數(shù)SKIPIF1<0的周期為SKIPIF1<0B.函數(shù)SKIPIF1<0圖象的一個(gè)對(duì)稱中心為SKIPIF1<0C.當(dāng)SKIPIF1<0時(shí),函數(shù)SKIPIF1<0的最小值為SKIPIF1<0D.函數(shù)SKIPIF1<0的極值點(diǎn)為SKIPIF1<0三、填空題33.(2023·全國·高三專題練習(xí))已知函數(shù)SKIPIF1<0的部分圖象如圖所示,將SKIPIF1<0的圖象向左平移SKIPIF1<0個(gè)單位得到SKIPIF1<0的圖象,若不等式SKIPIF1<0在SKIPIF1<0,上恒成立,則SKIPIF1<0的取值范圍是__.34.(2022秋·河北唐山·高三唐山一中校考階段練習(xí))函數(shù)SKIPIF1<0的圖象為C,以下結(jié)論中正確的是____寫出所有正確結(jié)論的編號(hào)).①圖象C關(guān)于直線SKIPIF1<0對(duì)稱;②圖象C關(guān)于點(diǎn)SKIPIF1<0對(duì)稱;③函數(shù)SKIPIF1<0在區(qū)間SKIPIF1<0內(nèi)是增函數(shù);④由SKIPIF1<0的圖象向右平移SKIPIF1<0個(gè)單位長度可以得到圖象C.35.(2022·全國·高三專題練習(xí))已知函數(shù)SKIPIF1<0,若關(guān)于x的方程SKIPIF1<0在SKIPIF1<0上有三個(gè)不同的實(shí)根,則實(shí)數(shù)m的取值范圍是_________.36.(2022秋·四川瀘州·高三四川省瀘縣第四中學(xué)??茧A段練習(xí))已知函數(shù)SKIPIF1<0的部分圖像如圖所示,則滿足SKIPIF1<0的最小正整數(shù)x的值為_______.四、解答題37.(2023·安徽馬鞍山·統(tǒng)考一模)已知條件:①SKIPIF1<0;②SKIPIF1<0;③SKIPIF1<0.在這三個(gè)條件中任選一個(gè),補(bǔ)充在下面的問題中,并解答.問題:在SKIPIF1<0中,角SKIPIF1<0,SKIPIF1<0,SKIPIF1<0所對(duì)的邊分別是SKIPIF1<0,SKIPIF1<0,SKIPIF1<0,滿足:______.注:如果選擇多個(gè)條件分別作答,按第一個(gè)解答計(jì)分.(1)求角SKIPIF1<0的大小;(2)若SKIPIF1<0為銳角三角形,SKIPIF1<0,求SKIPIF1<0的取值范圍.38.(2023·河北衡水·衡水市第二中學(xué)??寄M預(yù)測)已知函數(shù)SKIPIF1<0,SKIPIF1<0,SKIPIF1<0與SKIPIF1<0均在區(qū)間SKIPIF1<0上單調(diào)遞增,若SKIPIF1<0的最大值為SKIPIF1<0(1)求SKIPIF1<0的值(2)在不等腰SKIPIF1<0中,角A,B,C所對(duì)的邊分別為a,b,c,若SKIPIF1<0,證明:SKIPIF1<039.(2022·四川遂寧·射

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