新高考數(shù)學(xué)二輪復(fù)習(xí)解答題培優(yōu)練習(xí)專題03 三角函數(shù)的圖象與性質(zhì)（零點(diǎn)或根的問題）(典型題型歸類訓(xùn)練)（原卷版）

專題03三角函數(shù)的圖象與性質(zhì)（零點(diǎn)或根的問題）(典型題型歸類訓(xùn)練)目錄TOC\o"1-1"\h\u一、必備秘籍 1二、典型題型 1三、專項(xiàng)訓(xùn)練 3一、必備秘籍SKIPIF1<0實(shí)根問題，換元法令SKIPIF1<0將函數(shù)SKIPIF1<0化簡為SKIPIF1<0，在利用正弦函數(shù)SKIPIF1<0的圖象來解決交點(diǎn)（根，零點(diǎn)）的問題.二、典型題型1．（2023·四川成都·石室中學(xué)校考模擬預(yù)測）函數(shù)SKIPIF1<0的圖象由函數(shù)SKIPIF1<0的圖象向左平移SKIPIF1<0個(gè)單位長度得到，則SKIPIF1<0的圖象與直線SKIPIF1<0的交點(diǎn)個(gè)數(shù)為（

）A．1 B．2 C．3 D．42．（2023·浙江·校聯(lián)考二模）函數(shù)SKIPIF1<0的圖象向左平移SKIPIF1<0個(gè)單位長度后對應(yīng)的函數(shù)是奇函數(shù)，函數(shù)SKIPIF1<0．若關(guān)于x的方程SKIPIF1<0在SKIPIF1<0內(nèi)有兩個(gè)不同的解α，β，則SKIPIF1<0的值為（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<03．（2023·河南·校聯(lián)考模擬預(yù)測）已知函數(shù)SKIPIF1<0滿足SKIPIF1<0，若SKIPIF1<0在區(qū)間SKIPIF1<0上恰有3個(gè)零點(diǎn)，則實(shí)數(shù)t的取值范圍為（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<04．（2023·上海嘉定·?？既＃┤絷P(guān)于SKIPIF1<0的方程SKIPIF1<0在SKIPIF1<0上有實(shí)數(shù)解，則實(shí)數(shù)SKIPIF1<0的取值范圍是.5．（2023·全國·長郡中學(xué)校聯(lián)考模擬預(yù)測）將函數(shù)SKIPIF1<0圖象上各點(diǎn)的橫坐標(biāo)變?yōu)樵瓉淼腟KIPIF1<0倍，然后再向右平移SKIPIF1<0個(gè)單位得到函數(shù)SKIPIF1<0的圖象，則SKIPIF1<0的解析式為；若方程SKIPIF1<0在SKIPIF1<0的解為SKIPIF1<0、SKIPIF1<0，則SKIPIF1<0.6．（2023·黑龍江哈爾濱·哈爾濱市第六中學(xué)校?？既＃┮阎瘮?shù)SKIPIF1<0，其圖象的一條對稱軸與相鄰對稱中心的橫坐標(biāo)相差SKIPIF1<0，______，從以下兩個(gè)條件中任選一個(gè)補(bǔ)充在空白橫線中.①函數(shù)SKIPIF1<0的圖象向左平移SKIPIF1<0個(gè)單位長度后得到的圖象關(guān)于y軸對稱且SKIPIF1<0；②函數(shù)SKIPIF1<0的圖象的一個(gè)對稱中心為SKIPIF1<0且SKIPIF1<0.(1)求函數(shù)SKIPIF1<0的解析式；(2)將函數(shù)SKIPIF1<0圖象上所有點(diǎn)的橫坐標(biāo)變?yōu)樵瓉淼腟KIPIF1<0倍，縱坐標(biāo)不變，得到函數(shù)SKIPIF1<0的圖象，若函數(shù)SKIPIF1<0在區(qū)間SKIPIF1<0上恰有3個(gè)零點(diǎn)，求t的取值范圍.7．（2023秋·新疆烏魯木齊·高三烏魯木齊市第70中?？茧A段練習(xí)）已知函數(shù)SKIPIF1<0（其中SKIPIF1<0）的部分圖像如圖所示，將函數(shù)SKIPIF1<0的圖象向右平移SKIPIF1<0個(gè)單位長度，得到函數(shù)SKIPIF1<0的圖象．

(1)求SKIPIF1<0與SKIPIF1<0的解析式；(2)令SKIPIF1<0，求方程SKIPIF1<0在區(qū)間SKIPIF1<0內(nèi)的所有實(shí)數(shù)解的和．三、專項(xiàng)訓(xùn)練1．（2023·陜西西安·西安一中校聯(lián)考模擬預(yù)測）將函數(shù)SKIPIF1<0圖象所有點(diǎn)的縱坐標(biāo)伸長到原來的SKIPIF1<0倍，并沿x軸向左平移SKIPIF1<0個(gè)單位長度，再向上平移2個(gè)單位長度得到SKIPIF1<0的圖象．若SKIPIF1<0的圖象關(guān)于點(diǎn)SKIPIF1<0對稱，則函數(shù)SKIPIF1<0在SKIPIF1<0上零點(diǎn)的個(gè)數(shù)是（

）．A．1 B．2 C．3 D．42．（多選）（2023·山東菏澤·山東省鄄城縣第一中學(xué)?？既＃┮阎瘮?shù)SKIPIF1<0，把函數(shù)的圖象向右平移SKIPIF1<0個(gè)單位長度，得到函數(shù)SKIPIF1<0的圖象，若SKIPIF1<0時(shí)，方程SKIPIF1<0有實(shí)根，則實(shí)數(shù)SKIPIF1<0的取值可以為（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<03．（多選）（2023·福建三明·統(tǒng)考三模）已知函數(shù)SKIPIF1<0的圖象與直線SKIPIF1<0的相鄰兩個(gè)交點(diǎn)的距離為SKIPIF1<0，且對于任意SKIPIF1<0，不等式SKIPIF1<0恒成立，則（

）A．SKIPIF1<0B．SKIPIF1<0的取值范圍為SKIPIF1<0C．SKIPIF1<0在區(qū)間SKIPIF1<0上單調(diào)遞增D．若實(shí)數(shù)SKIPIF1<0使得方程SKIPIF1<0在SKIPIF1<0恰有SKIPIF1<0，SKIPIF1<0，SKIPIF1<0三個(gè)實(shí)數(shù)根，則SKIPIF1<0的最小值為SKIPIF1<04．（2023·黑龍江大慶·大慶中學(xué)?？寄M預(yù)測）將函數(shù)SKIPIF1<0的圖象向左平移SKIPIF1<0個(gè)單位得到函數(shù)SKIPIF1<0的圖象，若SKIPIF1<0在區(qū)間SKIPIF1<0上有且僅有一個(gè)零點(diǎn)，則實(shí)數(shù)m的一個(gè)取值為.5．（2023·陜西咸陽·武功縣普集高級(jí)中學(xué)?？寄M預(yù)測）已知SKIPIF1<0，當(dāng)SKIPIF1<0（其中SKIPIF1<0）時(shí)，SKIPIF1<0有且只有一個(gè)解，則SKIPIF1<0的取值范圍是.6．（2023·遼寧鞍山·鞍山一中?？级＃┖瘮?shù)SKIPIF1<0的部分圖象如圖所示．

(1)求函數(shù)SKIPIF1<0的解析式；(2)將函數(shù)SKIPIF1<0的圖象先向右平移SKIPIF1<0個(gè)單位，再將所有點(diǎn)的橫坐標(biāo)縮短為原來的SKIPIF1<0（縱坐標(biāo)不變），得到函數(shù)SKIPIF1<0的圖象，若關(guān)于SKIPIF1<0的方程SKIPIF1<0在SKIPIF1<0上有兩個(gè)不等實(shí)根SKIPIF1<0，求實(shí)數(shù)SKIPIF1<0的取值范圍，并求SKIPIF1<0的值．7．（2023·寧夏銀川·?？寄M預(yù)測）已知函數(shù)SKIPIF1<0（SKIPIF1<0，SKIPIF1<0）.再從條件①、條件②、條件③這三個(gè)條件中選擇能確定函數(shù)SKIPIF1<0的解析式的兩個(gè)作為已知.條件①：函數(shù)SKIPIF1<0的最小正周期為SKIPIF1<0；條件②：函數(shù)SKIPIF1<0的圖象經(jīng)過點(diǎn)SKIPIF1<0；條件③：函數(shù)SKIPIF1<0的最大值為SKIPIF1<0.(1)求SKIPIF1<0的解析式及最小值；(2)若函數(shù)SKIPIF1<0在區(qū)間SKIPIF1<0（SKIPIF1<0）上有且僅有1個(gè)零點(diǎn)，求SKIPIF1<0的取值范圍.8．（2023·福建寧德·?？寄M預(yù)測）已知函數(shù)SKIPIF1<0.(1)若方程SKIPIF1<0在SKIPIF1<0上有且只有一個(gè)實(shí)數(shù)根，求實(shí)數(shù)m的取值范圍；9．（2023秋·遼寧·高三校聯(lián)考階段練習(xí)）已知曲線SKIPIF1<0（SKIPIF1<0，SKIPIF1<0）相鄰的兩條對稱軸之間的距離為SKIPIF1<0，若將函數(shù)SKIPIF1<0的圖象先向左平移SKIPIF1<0個(gè)單位，再向下平移SKIPIF1<0個(gè)單位，得到函數(shù)SKIPIF1<0的圖象，且SKIPIF1<0為奇函數(shù).(1)求函數(shù)SKIPIF1<0的的解析式和其圖象的對稱中心；(2)若關(guān)于SKIPIF1<0的方程SKIPIF1<0在區(qū)間SKIPIF1<0上有兩個(gè)不相等的實(shí)數(shù)根，求實(shí)數(shù)SKIPIF1<0的取值范圍.10．（2023秋·安徽六安·高三六安一中?？茧A段練習(xí)）已知函數(shù)SKIPIF1<0(1)求函數(shù)SKIPIF1<0在區(qū)間SKIPIF1<0上的單調(diào)遞減區(qū)間；(2)將函數(shù)SKIPIF1<0的圖象上所有的點(diǎn)向右平移SKIPIF1<0個(gè)單位，再將所得圖象上每一個(gè)點(diǎn)的橫坐標(biāo)變?yōu)樵瓉淼腟KIPIF1<0倍（縱坐標(biāo)不變），再向上平移SKIPIF1<0個(gè)單位，得到函數(shù)SKIPIF1<0的圖象.當(dāng)SKIPIF1<0時(shí)，方程SKIPIF1<0恰有三個(gè)不相等的實(shí)數(shù)根SKIPIF1<0、SKIPIF1<0、SKIPIF1<0，求實(shí)數(shù)SKIPIF1<0的取值范圍和SKIPIF1<0的值.11．（2023秋·河南新鄉(xiāng)·高三衛(wèi)輝一中校聯(lián)考階段練習(xí)）已知函數(shù)SKIPIF1<0相鄰兩條對稱軸的距離為SKIPIF1<0，將SKIPIF1<0的圖象向右平移SKIPIF1<0個(gè)單位長度，得到函數(shù)SKIPIF1<0的圖象，且SKIPIF1<0的圖象關(guān)于原點(diǎn)對稱．(1)求SKIPIF1<0；(2)設(shè)函數(shù)SKIPIF1<0，當(dāng)SKIPIF1<0時(shí)，方程SKIPIF1<0有且僅有兩個(gè)實(shí)數(shù)根SKIPIF1<0，求實(shí)數(shù)SKIPIF1<0的取值范圍．12．（2023秋·安徽六安·高三六安二中校聯(lián)考階段練習(xí)）已知SKIPIF1<0，其中SKIPIF1<0，SKIPIF1<0，SKIPIF1<0，且滿足SKIPIF1<0，SKIPIF1<0．(1)求SKIPIF1<0的解析式；(2)若關(guān)于SKIPIF1<0的方程SKIPIF1<0在區(qū)間SKIPIF1<0上總有實(shí)數(shù)解，求實(shí)數(shù)SKIPIF1<0的取值范圍．13．（2023春·黑龍江齊齊哈爾·高一齊齊哈爾中學(xué)?？计谥校┮阎瘮?shù)SKIPIF1<0的最小正周期為SKIPIF1<0.(1)求SKIPIF1<0的解析式及對稱軸方程；(2)若關(guān)于x的方程SKIPIF1<0在SKIPIF1<0上有兩個(gè)不等實(shí)數(shù)解SKIPIF1<0，SKIPIF1<0.①求實(shí)數(shù)m的取值范圍；②求SKIPIF1<0的值.14．（2023秋·內(nèi)蒙古通遼·高三?？茧A段練習(xí)）已知函數(shù)SKIPIF1<0．(1)求SKIPIF1<0的最小正周期．(2)求SKIPIF1<0的單調(diào)遞增區(qū)間．(3)若關(guān)于SKIPIF1<0的方程SKIPIF1<0在SKIPIF1<0上有解，求實(shí)數(shù)m的取值范圍．15．（2023·全國·高三專題練習(xí)）已知向量SKIPIF1<0，函數(shù)SKIPIF1<0，SKIPIF1<0．(1)當(dāng)SKIPIF1<0時(shí)，求SKIPIF1<0的值；(2)若SKIPIF1<0的最小值為