新高考數(shù)學(xué)二輪復(fù)習(xí)重難點3-1 三角函數(shù)中ω的取值范圍問題（8題型+滿分技巧+限時檢測）（原卷版）

重難點3-1三角函數(shù)中ω的取值范圍問題三角函數(shù)是高考的必考考點，其中求ω取值范圍問題是熱門考點。主要結(jié)合函數(shù)的單調(diào)性、對稱性、極值與最值、零點等考查，需要考生能夠熟練應(yīng)用三角函數(shù)的基本性質(zhì)和圖象。根據(jù)近幾年新高考的考查情況，多在單選題與多選題中出現(xiàn)，難度較大?！绢}型1根據(jù)圖象平移求ω取值范圍】滿分技巧結(jié)合圖象平移求ω的取值范圍的常見類型及解題思路1、平移后與原圖象重合思路1：平移長度即為原函數(shù)周期的整倍數(shù)；思路2：平移前的函數(shù)=平移后的函數(shù).2、平移后與新圖象重合：平移后的函數(shù)=新的函數(shù).3、平移后的函數(shù)與原圖象關(guān)于軸對稱：平移后的函數(shù)為偶函數(shù)；4、平移后的函數(shù)與原函數(shù)關(guān)于軸對稱：平移前的函數(shù)=平移后的函數(shù)SKIPIF1<0；5、平移后過定點：將定點坐標(biāo)代入平移后的函數(shù)中?！纠?】（2024·云南楚雄·楚雄彝族自治州民族中學(xué)?？家荒＃⒑瘮?shù)SKIPIF1<0（SKIPIF1<0）的圖象向右平移SKIPIF1<0個單位長度后與函數(shù)SKIPIF1<0的圖象重合，則SKIPIF1<0的最小值為（）A．1B．2C．4D．5【變式1-1】（2024·全國·高三專題練習(xí)）將函數(shù)SKIPIF1<0的圖象分別向左、向右各平移SKIPIF1<0個單位長度后，所得的兩個圖象對稱軸重合，則SKIPIF1<0的最小值為（）A．3B．4C．5D．6【變式1-2】（2023·河南南陽·南陽中學(xué)?？既＃┒x運算：SKIPIF1<0，將函數(shù)SKIPIF1<0的圖像向左平移SKIPIF1<0個單位，所得圖像對應(yīng)的函數(shù)為偶函數(shù)，則SKIPIF1<0的最小正值是．【變式1-3】（2023·全國·高三專題練習(xí)）將函數(shù)SKIPIF1<0的圖象向右平移SKIPIF1<0個單位長度后，所得到的圖象與原圖象關(guān)于x軸對稱，則SKIPIF1<0的最小值為（）A．SKIPIF1<0B．3C．6D．9【變式1-4】（2023·江西宜春·高二宜豐中學(xué)校考階段練習(xí)）已知函數(shù)SKIPIF1<0，將SKIPIF1<0的圖象向右平移SKIPIF1<0個單位得到函數(shù)SKIPIF1<0的圖象，點SKIPIF1<0，SKIPIF1<0，SKIPIF1<0是SKIPIF1<0與SKIPIF1<0圖象的連續(xù)相鄰的三個交點，若SKIPIF1<0是鈍角三角形，則SKIPIF1<0的取值范圍是（）A．SKIPIF1<0B．SKIPIF1<0C．SKIPIF1<0D．SKIPIF1<0【題型2根據(jù)單調(diào)性求ω取值范圍】滿分技巧已知函數(shù)y=Asin(ωx+φ)(A>0,ω>0)，在[x1,x2]第一步：根據(jù)題意可知區(qū)間[x1即x2?x第二步：以單調(diào)遞增為例，利用ωx1+φ,ωx第三步：結(jié)合第一步求出的ω的范圍對k進(jìn)行賦值，從而求出ω（不含參數(shù)）的取值范圍.【例2】（2024·云南保山·高三統(tǒng)考期末）已知SKIPIF1<0（SKIPIF1<0）在區(qū)間SKIPIF1<0上單調(diào)遞增，則SKIPIF1<0的取值范圍為.【變式2-1】（2023·陜西商洛·鎮(zhèn)安中學(xué)?？寄M預(yù)測）若函數(shù)SKIPIF1<0在區(qū)間SKIPIF1<0上單調(diào)遞減，則正數(shù)SKIPIF1<0的取值范圍為（）A．SKIPIF1<0B．SKIPIF1<0C．SKIPIF1<0D．SKIPIF1<0【變式2-2】（2023·陜西漢中·高三西鄉(xiāng)縣第一中學(xué)校聯(lián)考期中）已知SKIPIF1<0，函數(shù)SKIPIF1<0在SKIPIF1<0單調(diào)遞減，則SKIPIF1<0的取值范圍為（）A．SKIPIF1<0B．SKIPIF1<0C．SKIPIF1<0D．SKIPIF1<0【變式2-3】（2023·四川·高三校聯(lián)考階段練習(xí)）已知函數(shù)SKIPIF1<0（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<0B．SKIPIF1<0C．SKIPIF1<0D．SKIPIF1<0【變式2-4】（2024·廣東肇慶·統(tǒng)考模擬預(yù)測）（多選）已知SKIPIF1<0，函數(shù)SKIPIF1<0，SKIPIF1<0，若SKIPIF1<0在區(qū)間SKIPIF1<0上單調(diào)遞增，則SKIPIF1<0的可能取值為（）A．SKIPIF1<0B．SKIPIF1<0C．2D．4【題型3根據(jù)對稱軸求ω取值范圍】滿分技巧三角函數(shù)兩條相鄰對稱軸或兩個相鄰對稱中心之間的“水平間隔”為T2，相鄰的對稱軸和對稱中心之間的“水平間隔”為T4，也就是說，我們可以根據(jù)三角函數(shù)的對稱性來研究其周期性，進(jìn)而可以研究【例3】（2023·安徽六安·高三六安一中?？茧A段練習(xí)）已知函數(shù)SKIPIF1<0在區(qū)間SKIPIF1<0恰有兩條對稱軸，則SKIPIF1<0的取值范圍（）A．SKIPIF1<0B．SKIPIF1<0C．SKIPIF1<0D．SKIPIF1<0【變式3-1】（2024·云南德宏·高三統(tǒng)考期末）已知函數(shù)SKIPIF1<0在區(qū)間SKIPIF1<0上恰有兩條對稱軸，則SKIPIF1<0的取值范圍是（）A．SKIPIF1<0B．SKIPIF1<0C．SKIPIF1<0D．SKIPIF1<0【變式3-2】（2023·湖北黃岡·高三?？计谥校┤艉瘮?shù)SKIPIF1<0在區(qū)間SKIPIF1<0上恰有唯一對稱軸，則ω的取值范圍為（）A．SKIPIF1<0B．SKIPIF1<0C．SKIPIF1<0D．SKIPIF1<0【變式3-3】（2023·廣西·模擬預(yù)測）若函數(shù)SKIPIF1<0（SKIPIF1<0，SKIPIF1<0）滿足SKIPIF1<0，且SKIPIF1<0，則SKIPIF1<0的最小值為（）A．1B．2C．3D．4【變式3-4】（2023·全國·高三校聯(lián)考階段練習(xí)）已知函數(shù)SKIPIF1<0的圖象在SKIPIF1<0上有且僅有3條對稱軸，則實數(shù)SKIPIF1<0的取值范圍為.【題型4根據(jù)對稱中心求ω取值范圍】滿分技巧三角函數(shù)兩條相鄰對稱軸或兩個相鄰對稱中心之間的“水平間隔”為T2，相鄰的對稱軸和對稱中心之間的“水平間隔”為T4，也就是說，我們可以根據(jù)三角函數(shù)的對稱性來研究其周期性，進(jìn)而可以研究【例4】（2022·四川綿陽·統(tǒng)考模擬預(yù)測）若存在實數(shù)SKIPIF1<0，使得函數(shù)SKIPIF1<0(SKIPIF1<0>0)的圖象的一個對稱中心為(SKIPIF1<0，0)，則ω的取值范圍為（）A．SKIPIF1<0B．SKIPIF1<0C．SKIPIF1<0D．SKIPIF1<0【變式4-1】（2023·全國·高三專題練習(xí)）已知函數(shù)SKIPIF1<0的圖象的一個對稱中心的橫坐標(biāo)在區(qū)間SKIPIF1<0內(nèi)，且兩個相鄰對稱中心之間的距離大于SKIPIF1<0，則SKIPIF1<0的取值范圍為（）A．SKIPIF1<0B．SKIPIF1<0C．SKIPIF1<0D．SKIPIF1<0【變式4-2】（2022·全國·高三專題練習(xí)）已知函數(shù)SKIPIF1<0在SKIPIF1<0內(nèi)不存在對稱中心，則SKIPIF1<0的取值范圍為（）．A．SKIPIF1<0B．SKIPIF1<0C．SKIPIF1<0D．SKIPIF1<0【變式4-3】（2023·四川·校考模擬預(yù)測）已知函數(shù)SKIPIF1<0的圖象在SKIPIF1<0上恰有一條對稱軸和一個對稱中心，則實數(shù)SKIPIF1<0的取值范圍為.【變式4-4】（2022·江蘇南京·高三江浦高級中學(xué)校聯(lián)考階段練習(xí)）將函數(shù)SKIPIF1<0的圖象向右平移SKIPIF1<0個周期后，所得圖象恰有SKIPIF1<0個對稱中心在區(qū)間SKIPIF1<0內(nèi)，則SKIPIF1<0的取值范圍為.【題型5根據(jù)最值求ω取值范圍】滿分技巧根據(jù)三角函數(shù)的最值或值域求解參數(shù)問題是，要靈活運用整體的思想，將問題轉(zhuǎn)化在基本函數(shù)SKIPIF1<0、SKIPIF1<0、SKIPIF1<0上，借助函數(shù)圖象性質(zhì)來處理會更加明了。注意對SKIPIF1<0正負(fù)的討論。【例5】（2024·浙江溫州·統(tǒng)考一模）若函數(shù)SKIPIF1<0，SKIPIF1<0的值域為SKIPIF1<0，則SKIPIF1<0的取值范圍是（）A．SKIPIF1<0B．SKIPIF1<0C．SKIPIF1<0D．SKIPIF1<0【變式5-1】（2024·廣東梅州·高三廣東梅縣東山中學(xué)校考期末）已知函數(shù)SKIPIF1<0在區(qū)間SKIPIF1<0上有且只有一個最大值和一個最小值，則SKIPIF1<0的取值范圍是（）A．SKIPIF1<0B．SKIPIF1<0C．SKIPIF1<0D．SKIPIF1<0【變式5-2】（2024·廣東深圳·高三統(tǒng)考期末）若函數(shù)SKIPIF1<0在SKIPIF1<0有最小值，沒有最大值，則SKIPIF1<0的取值范圍是（）A．SKIPIF1<0B．SKIPIF1<0C．SKIPIF1<0D．SKIPIF1<0【變式5-3】（2023·山東·高三校聯(lián)考階段練習(xí)）已知函數(shù)SKIPIF1<0在區(qū)間SKIPIF1<0內(nèi)不存在最值，且在區(qū)間SKIPIF1<0上，滿足SKIPIF1<0恒成立，則SKIPIF1<0的取值范圍是（）A．SKIPIF1<0B．SKIPIF1<0C．SKIPIF1<0D．SKIPIF1<0【變式5-4】（2023·安徽·高三池州市第一中學(xué)校聯(lián)考階段練習(xí)）（多選）將函數(shù)SKIPIF1<0的圖象向左平移SKIPIF1<0個單位可得到函數(shù)SKIPIF1<0的圖象，若SKIPIF1<0在區(qū)間SKIPIF1<0內(nèi)有最值，則實數(shù)SKIPIF1<0的取值范圍可能為（）A．SKIPIF1<0B．SKIPIF1<0C．SKIPIF1<0D．SKIPIF1<0【題型6根據(jù)極值求ω取值范圍】【例6】（2024·全國·模擬預(yù)測）若函數(shù)SKIPIF1<0在區(qū)間SKIPIF1<0上有且僅有一個極值點，則SKIPIF1<0的取值范圍為.【變式6-1】（2023·江蘇連云港·高三統(tǒng)考期中）若函數(shù)SKIPIF1<0在SKIPIF1<0上存在唯一的極值點，則正數(shù)SKIPIF1<0的取值范圍是（）A．SKIPIF1<0B．SKIPIF1<0C．SKIPIF1<0D．SKIPIF1<0【變式6-2】（2023·上海奉賢·統(tǒng)考一模）設(shè)函數(shù)SKIPIF1<0在區(qū)間SKIPIF1<0上恰有三個極值點，則SKIPIF1<0的取值范圍為．【變式6-3】（2023·陜西西安·高三校聯(lián)考階段練習(xí)）已知函數(shù)SKIPIF1<0在SKIPIF1<0上至少有3個極值點，則實數(shù)SKIPIF1<0的取值范圍為．【變式6-4】（2023·吉林·統(tǒng)考一模）已知函數(shù)SKIPIF1<0在區(qū)間SKIPIF1<0上有且僅有4個極大值點，則正實數(shù)SKIPIF1<0的取值范圍為（）A．SKIPIF1<0B．SKIPIF1<0C．SKIPIF1<0D．SKIPIF1<0【題型7根據(jù)零點求ω取值范圍】滿分技巧已知三角函數(shù)的零點個數(shù)問題求ω的取值范圍對于區(qū)間長度為定值的動區(qū)間，若區(qū)間上至少含有SKIPIF1<0個零點，需要確定含有SKIPIF1<0個零點的區(qū)間長度，一般和周期相關(guān)，若在在區(qū)間至多含有SKIPIF1<0個零點，需要確定包含SKIPIF1<0個零點的區(qū)間長度的最小值．【例7】（2023·江蘇淮安·高三馬壩高中?？计谥校┮阎瘮?shù)SKIPIF1<0（SKIPIF1<0）在SKIPIF1<0上恰有2個零點，則SKIPIF1<0的取值范圍為（）A．SKIPIF1<0B．SKIPIF1<0C．SKIPIF1<0D．SKIPIF1<0【變式7-1】（2024·內(nèi)蒙古鄂爾多斯·高三統(tǒng)考期末）已知函數(shù)SKIPIF1<0，若方程SKIPIF1<0在區(qū)間SKIPIF1<0上恰有3個實根，則SKIPIF1<0的取值范圍是（）A．SKIPIF1<0B．SKIPIF1<0C．SKIPIF1<0D．SKIPIF1<0【變式7-2】（2024·廣東汕頭·高三統(tǒng)考期末）已知函數(shù)SKIPIF1<0在區(qū)間SKIPIF1<0上恰有三個零點，則SKIPIF1<0的取值范圍是.【變式7-3】（2024·全國·高三開學(xué)考試）設(shè)函數(shù)SKIPIF1<0，且函數(shù)SKIPIF1<0在SKIPIF1<0恰好有5個零點，則正實數(shù)SKIPIF1<0的取值范圍是【變式7-4】（2022·河南·高三校聯(lián)考階段練習(xí)）已知函數(shù)SKIPIF1<0，SKIPIF1<0，且SKIPIF1<0在SKIPIF1<0上恰有100個零點，則SKIPIF1<0的取值范圍是（）A．SKIPIF1<0B．SKIPIF1<0C．SKIPIF1<0D．SKIPIF1<0【題型8結(jié)合函數(shù)性質(zhì)綜合考查】【例8】（2024·全國·模擬預(yù)測）將函數(shù)SKIPIF1<0的圖象先向右平移SKIPIF1<0個單位長度，再把所得函數(shù)圖象的橫坐標(biāo)變?yōu)樵瓉淼腟KIPIF1<0，縱坐標(biāo)不變，得到函數(shù)SKIPIF1<0的圖象．若函數(shù)SKIPIF1<0在SKIPIF1<0上沒有零點，則SKIPIF1<0的取值范圍是（）A．SKIPIF1<0B．SKIPIF1<0C．SKIPIF1<0D．SKIPIF1<0【變式8-1】（2024·江西上饒·高三?？茧A段練習(xí)）已知函數(shù)SKIPIF1<0在區(qū)間SKIPIF1<0上單調(diào)遞增，且SKIPIF1<0在區(qū)間SKIPIF1<0上只取得一次最大值，則SKIPIF1<0的取值范圍為（）A．SKIPIF1<0B．SKIPIF1<0C．SKIPIF1<0D．SKIPIF1<0【變式8-2】（2024·山西晉城·統(tǒng)考一模）若函數(shù)SKIPIF1<0在SKIPIF1<0上至少有兩個極大值點和兩個零點，則SKIPIF1<0的取值范圍為．【變式8-3】（2024·遼寧大連·高三統(tǒng)考期末）已知函數(shù)SKIPIF1<0滿足下列條件：①對任意SKIPIF1<0恒成立；②SKIPIF1<0在區(qū)間SKIPIF1<0上是單調(diào)函數(shù)；③經(jīng)過點SKIPIF1<0的任意一條直線與函數(shù)SKIPIF1<0圖像都有交點，則SKIPIF1<0的取值范圍是（）A．SKIPIF1<0B．SKIPIF1<0C．SKIPIF1<0D．SKIPIF1<0（建議用時：60分鐘）1．（2023·江蘇鹽城·高三統(tǒng)考期中）若函數(shù)SKIPIF1<0在SKIPIF1<0上單調(diào)，則SKIPIF1<0的取值范圍是（）A．SKIPIF1<0B．SKIPIF1<0C．SKIPIF1<0D．SKIPIF1<02．（2023·陜西漢中·高三校聯(lián)考期中）已知SKIPIF1<0，函數(shù)SKIPIF1<0在SKIPIF1<0單調(diào)遞減，則SKIPIF1<0的取值范圍為（）A．SKIPIF1<0B．SKIPIF1<0C．SKIPIF1<0D．SKIPIF1<03．（2024·黑龍江哈爾濱·高三哈爾濱市第六中學(xué)校校聯(lián)考期末）設(shè)函數(shù)SKIPIF1<0，已知方程SKIPIF1<0在SKIPIF1<0上有且僅有2個根，則SKIPIF1<0的取值范圍是（）A．SKIPIF1<0B．SKIPIF1<0C．SKIPIF1<0D．SKIPIF1<04．（2023·黑龍江哈爾濱·高三哈爾濱市第十三中學(xué)校?？计谥校┤艉瘮?shù)SKIPIF1<0在區(qū)間SKIPIF1<0上既有最大值，又有最小值，則SKIPIF1<0的取值范圍為（）A．SKIPIF1<0B．SKIPIF1<0C．SKIPIF1<0D．SKIPIF1<05．（2023·遼寧沈陽·東北育才學(xué)校校考模擬預(yù)測）已知函數(shù)SKIPIF1<0．若SKIPIF1<0在區(qū)間SKIPIF1<0內(nèi)沒有零點，則SKIPIF1<0的取值范圍是（）A．SKIPIF1<0B．SKIPIF1<0C．SKIPIF1<0D．SKIPIF1<06．（2023·福建福州·高三校聯(lián)考期中）設(shè)函數(shù)SKIPIF1<0在區(qū)間SKIPIF1<0恰有三個極值點，則SKIPIF1<0的取值范圍為（）A．SKIPIF1<0B．SKIPIF1<0C．SKIPIF1<0D．SKIPIF1<07．（2024·全國·模擬預(yù)測）已知函數(shù)SKIPIF1<0在區(qū)間SKIPIF1<0上單調(diào)，且在區(qū)間SKIPIF1<0上有5個零點，則SKIPIF1<0的取值范圍為（）A．SKIPIF1<0B．SKIPIF1<0C．SKIPIF1