新高考數(shù)學(xué)一輪復(fù)習(xí)提升訓(xùn)練5.3 三角函數(shù)的性質(zhì)（精講）（原卷版）

5.3三角函數(shù)的性質(zhì)（精講）（提升版）思維導(dǎo)圖思維導(dǎo)圖考點(diǎn)呈現(xiàn)考點(diǎn)呈現(xiàn)例題剖析例題剖析考點(diǎn)一值域【例1-1】（2022·湖南·長郡中學(xué)高三階段練習(xí)）函數(shù)SKIPIF1<0（SKIPIF1<0）的圖象向左平移SKIPIF1<0個(gè)單位后關(guān)于直線SKIPIF1<0對稱，則函數(shù)SKIPIF1<0在區(qū)間SKIPIF1<0上的最小值為（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<0【例1-2】（2022·全國·高三專題練習(xí)）函數(shù)SKIPIF1<0的最大值為（

）A．1 B．SKIPIF1<0 C．SKIPIF1<0 D．3【例1-3】（2021·河南南陽·高三期末）已知SKIPIF1<0，若SKIPIF1<0對任意SKIPIF1<0恒成立，則實(shí)數(shù)SKIPIF1<0的取值范圍為(

)A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<0【例1-4】（2022·陜西·武功縣普集高級中學(xué)高三階段練習(xí)（理））函數(shù)SKIPIF1<0在SKIPIF1<0內(nèi)恰有兩個(gè)最小值點(diǎn)，則SKIPIF1<0的范圍是（

）A．SKIPIF1<0 B．SKIPIF1<0C．SKIPIF1<0 D．SKIPIF1<0【一隅三反】1．（2021·江蘇泰州·高三階段練習(xí)）已知函數(shù)SKIPIF1<0，SKIPIF1<0的值域?yàn)镾KIPIF1<0，則實(shí)數(shù)SKIPIF1<0的取值范圍為（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<02．（2022·河南焦作·二模）已知函數(shù)SKIPIF1<0，若方程SKIPIF1<0在區(qū)間SKIPIF1<0上恰有5個(gè)實(shí)根，則SKIPIF1<0的取值范圍是（

）A．SKIPIF1<0 B．SKIPIF1<0C．SKIPIF1<0 D．SKIPIF1<03．（2022·全國·高三專題練習(xí)）已知函SKIPIF1<0，對于任意的x1，x2∈R，都有f(x1)+f(x2)-2SKIPIF1<0≤0，若f(x)在[0，π]上的值域?yàn)镾KIPIF1<0，則實(shí)數(shù)ω的取值范圍為（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<0考點(diǎn)二伸縮平移【例2-1】（2022·河南洛陽·模擬預(yù)測（文））已知曲線SKIPIF1<0，SKIPIF1<0，為了得到曲線SKIPIF1<0，則對曲線SKIPIF1<0的變換正確的是（

）A．先把橫坐標(biāo)伸長到原來的2倍（縱坐標(biāo)不變），再把得到的曲線向右平移SKIPIF1<0個(gè)單位長度B．先把橫坐標(biāo)伸長到原來的2倍（縱坐標(biāo)不變），再把得到的曲線向左平移SKIPIF1<0個(gè)單位長度C．先把橫坐標(biāo)縮短到原來的SKIPIF1<0倍（縱坐標(biāo)不變），再把得到的曲線向右平移SKIPIF1<0個(gè)單位長度D．先把橫坐標(biāo)縮短到原來的SKIPIF1<0倍（縱坐標(biāo)不變），再把得到的曲線向左平移SKIPIF1<0個(gè)單位長度【例2-2】（2022·全國·高三專題練習(xí)）將函數(shù)SKIPIF1<0的圖象向左平移a(a>0)個(gè)單位長度得到函數(shù)g(x)=cos2x的圖象，則a的最小值為（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．π【一隅三反】1．（2022·陜西）已知函數(shù)SKIPIF1<0的最小正周期為SKIPIF1<0，若將其圖象向左平移SKIPIF1<0個(gè)單位長度后得到的圖象關(guān)于坐標(biāo)原點(diǎn)對稱，則SKIPIF1<0的圖象（

）A．關(guān)于點(diǎn)SKIPIF1<0對稱 B．關(guān)于SKIPIF1<0對稱 C．關(guān)于點(diǎn)SKIPIF1<0對稱 D．關(guān)于SKIPIF1<0對稱2．（2022·湖北·一模）函數(shù)SKIPIF1<0，先把函數(shù)SKIPIF1<0的圖像向左平移SKIPIF1<0個(gè)單位，再把圖像上各點(diǎn)的橫坐標(biāo)縮短到原來的SKIPIF1<0，得到函數(shù)SKIPIF1<0的圖像，則下列說法錯(cuò)誤的是（

）A．函數(shù)SKIPIF1<0是奇函數(shù)，最大值是2B．函數(shù)SKIPIF1<0在區(qū)間SKIPIF1<0上單調(diào)遞增C．函數(shù)SKIPIF1<0的圖像關(guān)于直線SKIPIF1<0對稱D．π是函數(shù)SKIPIF1<0的周期3．（2022·全國·模擬預(yù)測）若將函數(shù)SKIPIF1<0的圖象分別向左平移SKIPIF1<0個(gè)單位長度與向右平移SKIPIF1<0個(gè)單位長度，所得的兩個(gè)函數(shù)圖象恰好重合，則SKIPIF1<0的最小值為（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<0考點(diǎn)三三角函數(shù)的性質(zhì)【例3-1】（2022·全國·高三專題練習(xí)）（多選）下列函數(shù)中，以SKIPIF1<0為最小正周期的函數(shù)有（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<0【例3-2】（2020·河南）已知函數(shù)SKIPIF1<0的圖象與函數(shù)SKIPIF1<0圖象的對稱中心完全相同，則SKIPIF1<0（

）A．SKIPIF1<0 B．SKIPIF1<0 C．1 D．2【例3-3】（2022·四川·瀘縣五中二模（文））將SKIPIF1<0的圖象向左平移SKIPIF1<0個(gè)單位后得到SKIPIF1<0的圖象，則SKIPIF1<0有（

）A．為奇函數(shù)，在SKIPIF1<0上單調(diào)遞減B．為偶函數(shù)，在SKIPIF1<0上單調(diào)遞增C．周期為π，圖象關(guān)于點(diǎn)SKIPIF1<0對稱D．最大值為1，圖象關(guān)于直線SKIPIF1<0對稱【例3-4】（2022·山東青島·一模）已知函數(shù)SKIPIF1<0，將SKIPIF1<0的圖象先向左平移SKIPIF1<0個(gè)單位長度，然后再向下平移1個(gè)單位長度，得到函數(shù)SKIPIF1<0的圖象，若SKIPIF1<0圖象關(guān)于SKIPIF1<0對稱，則SKIPIF1<0為（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<0【一隅三反】1．（2022·全國·高三專題練習(xí)）（多選）下列函數(shù)中，圖象為軸對稱圖形的是（

）A．SKIPIF1<0 B．SKIPIF1<0C．SKIPIF1<0 D．SKIPIF1<02．（2022·北京西城·一模）將函數(shù)SKIPIF1<0的圖象向右平移SKIPIF1<0個(gè)單位所得函數(shù)圖象關(guān)于原點(diǎn)對稱，向左平移SKIPIF1<0個(gè)單位所得函數(shù)圖象關(guān)于SKIPIF1<0軸對稱，其中SKIPIF1<0，SKIPIF1<0，則SKIPIF1<0（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<03．（2022·北京·一模）已知函數(shù)SKIPIF1<0.從下列四個(gè)條件中選擇兩個(gè)作為已知，使函數(shù)SKIPIF1<0存在且唯一確定．(1)求SKIPIF1<0的解析式；(2)設(shè)SKIPIF1<0，求函數(shù)SKIPIF1<0在SKIPIF1<0上的單調(diào)遞增區(qū)間.條件①：SKIPIF1<0；條件②：SKIPIF1<0為偶函數(shù)；條件③：SKIPIF1<0的最大值為1；條件④：SKIPIF1<0圖象的相鄰兩條對稱軸之間的距離為SKIPIF1<0．注：如果選擇的條件不符合要求，第（1）問得0分；如果選擇多個(gè)符合要求的條件分別解答，按第一個(gè)解答計(jì)分.4．（2022·浙江浙江·二模）已知函數(shù)SKIPIF1<0，SKIPIF1<0．(1)求函數(shù)SKIPIF1<0的單調(diào)遞增區(qū)間；(2)求函數(shù)SKIPIF1<0的值域．考點(diǎn)四三角函數(shù)性質(zhì)與其他知識(shí)的綜合運(yùn)用【例4-1】（2022·江蘇蘇州）若函數(shù)SKIPIF1<0在區(qū)間[0，π)內(nèi)有且只有兩個(gè)極值點(diǎn)，則正數(shù)ω的取值范圍是（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<0【一隅三反】1．（2022·江蘇南通·模擬預(yù)測）已知函數(shù)SKIPIF1<0在區(qū)間SKIPIF1<0上無極值，則SKIPIF1<0的取值范圍是（

）A．（0，5] B．（0，5）C．（0，SKIPIF1<0） D．（0，SKIPIF1<0]2．（2022·陜西·西安中學(xué)模擬預(yù)測（文））已知函數(shù)SKIPIF1<0的部分