2021-2023年高考數(shù)學(xué)真題分類匯編專題09 三角函數(shù)（原卷版）

專題09三角函數(shù)知識(shí)點(diǎn)目錄知識(shí)點(diǎn)1：三角函數(shù)的圖像與性質(zhì)：奇偶性、單調(diào)性、奇偶性知識(shí)點(diǎn)2：值域與最值問(wèn)題知識(shí)點(diǎn)3：伸縮變換問(wèn)題知識(shí)點(diǎn)4：求SKIPIF1<0解析式問(wèn)題知識(shí)點(diǎn)5：三角恒等變換知識(shí)點(diǎn)6：SKIPIF1<0與SKIPIF1<0的取值與范圍問(wèn)題知識(shí)點(diǎn)7：弧長(zhǎng)公式近三年高考真題知識(shí)點(diǎn)1：三角函數(shù)的圖像與性質(zhì)：奇偶性、單調(diào)性、奇偶性1．（2023?全國(guó)）已知函數(shù)SKIPIF1<0，則SKIPIF1<0SKIPIF1<0A．SKIPIF1<0上單調(diào)遞增 B．SKIPIF1<0上單調(diào)遞增 C．SKIPIF1<0上單調(diào)遞減 D．SKIPIF1<0上單調(diào)遞增2．（2022?天津）已知SKIPIF1<0，關(guān)于該函數(shù)有下列四個(gè)說(shuō)法：①SKIPIF1<0的最小正周期為SKIPIF1<0；②SKIPIF1<0在SKIPIF1<0，SKIPIF1<0上單調(diào)遞增；③當(dāng)SKIPIF1<0，SKIPIF1<0時(shí)，SKIPIF1<0的取值范圍為SKIPIF1<0，SKIPIF1<0；④SKIPIF1<0的圖象可由SKIPIF1<0的圖象向左平移SKIPIF1<0個(gè)單位長(zhǎng)度得到．以上四個(gè)說(shuō)法中，正確的個(gè)數(shù)為SKIPIF1<0SKIPIF1<0A．1 B．2 C．3 D．43．（2021?北京）函數(shù)SKIPIF1<0是SKIPIF1<0SKIPIF1<0A．奇函數(shù)，且最大值為2 B．偶函數(shù)，且最大值為2 C．奇函數(shù)，且最大值為SKIPIF1<0 D．偶函數(shù)，且最大值為SKIPIF1<04．（2022?北京）已知函數(shù)SKIPIF1<0，則SKIPIF1<0SKIPIF1<0A．SKIPIF1<0在SKIPIF1<0，SKIPIF1<0上單調(diào)遞減 B．SKIPIF1<0在SKIPIF1<0，SKIPIF1<0上單調(diào)遞增 C．SKIPIF1<0在SKIPIF1<0上單調(diào)遞減 D．SKIPIF1<0在SKIPIF1<0，SKIPIF1<0上單調(diào)遞增5．（2021?新高考Ⅰ）下列區(qū)間中，函數(shù)SKIPIF1<0單調(diào)遞增的區(qū)間是SKIPIF1<0SKIPIF1<0A．SKIPIF1<0 B．SKIPIF1<0，SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<0，SKIPIF1<06．（2021?乙卷（文））函數(shù)SKIPIF1<0的最小正周期和最大值分別是SKIPIF1<0SKIPIF1<0A．SKIPIF1<0和SKIPIF1<0 B．SKIPIF1<0和2 C．SKIPIF1<0和SKIPIF1<0 D．SKIPIF1<0和27．（多選題）（2022?新高考Ⅱ）已知函數(shù)SKIPIF1<0的圖像關(guān)于點(diǎn)SKIPIF1<0，SKIPIF1<0中心對(duì)稱，則SKIPIF1<0SKIPIF1<0A．SKIPIF1<0在區(qū)間SKIPIF1<0單調(diào)遞減 B．SKIPIF1<0在區(qū)間SKIPIF1<0，SKIPIF1<0有兩個(gè)極值點(diǎn) C．直線SKIPIF1<0是曲線SKIPIF1<0的對(duì)稱軸 D．直線SKIPIF1<0是曲線SKIPIF1<0的切線8．（2022?上海）函數(shù)SKIPIF1<0的周期為．9．（2023?北京）已知函數(shù)SKIPIF1<0，SKIPIF1<0，SKIPIF1<0．（Ⅰ）若SKIPIF1<0，求SKIPIF1<0的值；（Ⅱ）若SKIPIF1<0在SKIPIF1<0，SKIPIF1<0上單調(diào)遞增，且SKIPIF1<0，再?gòu)臈l件①、條件②、條件③這三個(gè)條件中選擇一個(gè)作為已知，求SKIPIF1<0、SKIPIF1<0的值．條件①：SKIPIF1<0；條件②：SKIPIF1<0；條件③：SKIPIF1<0在SKIPIF1<0，SKIPIF1<0上單調(diào)遞減．注：如果選擇多個(gè)條件分別解答，按第一個(gè)解答計(jì)分．知識(shí)點(diǎn)2：值域與最值問(wèn)題10．（2021?浙江）設(shè)函數(shù)SKIPIF1<0．（Ⅰ）求函數(shù)SKIPIF1<0的最小正周期；（Ⅱ）求函數(shù)SKIPIF1<0在SKIPIF1<0，SKIPIF1<0上的最大值．11．（2023?上海）已知SKIPIF1<0，記SKIPIF1<0在SKIPIF1<0，SKIPIF1<0的最小值為SKIPIF1<0，在SKIPIF1<0，SKIPIF1<0的最小值為SKIPIF1<0，則下列情況不可能的是SKIPIF1<0SKIPIF1<0A．SKIPIF1<0，SKIPIF1<0 B．SKIPIF1<0，SKIPIF1<0 C．SKIPIF1<0，SKIPIF1<0 D．SKIPIF1<0，SKIPIF1<012．（2022年全國(guó)乙卷）函數(shù)fx=cosx+x+1sinx+1在區(qū)間A．?π2，π2 B．?3π13．（2021?浙江）已知SKIPIF1<0，SKIPIF1<0，SKIPIF1<0是互不相同的銳角，則在SKIPIF1<0，SKIPIF1<0，SKIPIF1<0三個(gè)值中，大于SKIPIF1<0的個(gè)數(shù)的最大值是SKIPIF1<0SKIPIF1<0A．0 B．1 C．2 D．3知識(shí)點(diǎn)3：伸縮變換問(wèn)題14．（2021?乙卷（文））把函數(shù)SKIPIF1<0圖像上所有點(diǎn)的橫坐標(biāo)縮短到原來(lái)的SKIPIF1<0倍，縱坐標(biāo)不變，再把所得曲線向右平移SKIPIF1<0個(gè)單位長(zhǎng)度，得到函數(shù)SKIPIF1<0的圖像，則SKIPIF1<0SKIPIF1<0A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<015．（2023?甲卷）已知SKIPIF1<0為函數(shù)SKIPIF1<0向左平移SKIPIF1<0個(gè)單位所得函數(shù)，則SKIPIF1<0與SKIPIF1<0的交點(diǎn)個(gè)數(shù)為SKIPIF1<0SKIPIF1<0A．1 B．2 C．3 D．416．（2022?浙江）為了得到函數(shù)SKIPIF1<0的圖象，只要把函數(shù)SKIPIF1<0圖象上所有的點(diǎn)SKIPIF1<0SKIPIF1<0A．向左平移SKIPIF1<0個(gè)單位長(zhǎng)度 B．向右平移SKIPIF1<0個(gè)單位長(zhǎng)度 C．向左平移SKIPIF1<0個(gè)單位長(zhǎng)度 D．向右平移SKIPIF1<0個(gè)單位長(zhǎng)度知識(shí)點(diǎn)4：求SKIPIF1<0解析式問(wèn)題17．（2023?乙卷）已知函數(shù)SKIPIF1<0在區(qū)間SKIPIF1<0，SKIPIF1<0單調(diào)遞增，直線SKIPIF1<0和SKIPIF1<0為函數(shù)SKIPIF1<0的圖像的兩條對(duì)稱軸，則SKIPIF1<0SKIPIF1<0A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<018．（2023?天津）已知函數(shù)SKIPIF1<0的一條對(duì)稱軸為直線SKIPIF1<0，一個(gè)周期為4，則SKIPIF1<0的解析式可能為SKIPIF1<0SKIPIF1<0A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<019．（2022?新高考Ⅰ）記函數(shù)SKIPIF1<0的最小正周期為SKIPIF1<0．若SKIPIF1<0，且SKIPIF1<0的圖像關(guān)于點(diǎn)SKIPIF1<0，SKIPIF1<0中心對(duì)稱，則SKIPIF1<0SKIPIF1<0A．1 B．SKIPIF1<0 C．SKIPIF1<0 D．320．（2023?新高考Ⅱ）已知函數(shù)SKIPIF1<0，如圖，SKIPIF1<0，SKIPIF1<0是直線SKIPIF1<0與曲線SKIPIF1<0的兩個(gè)交點(diǎn)，若SKIPIF1<0，則SKIPIF1<0．21．（2021?甲卷(文）已知函數(shù)SKIPIF1<0的部分圖像如圖所示，則SKIPIF1<0．22．（2021?甲卷（理））已知函數(shù)SKIPIF1<0的部分圖像如圖所示，則滿足條件SKIPIF1<0的最小正整數(shù)SKIPIF1<0為．知識(shí)點(diǎn)5：三角恒等變換23．（2023?新高考Ⅰ）已知SKIPIF1<0，SKIPIF1<0，則SKIPIF1<0SKIPIF1<0A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<024．（2023?新高考Ⅱ）已知SKIPIF1<0為銳角，SKIPIF1<0，則SKIPIF1<0SKIPIF1<0A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<025．（2023?乙卷（文））若SKIPIF1<0，SKIPIF1<0，則SKIPIF1<0．26．（2023?上海）已知SKIPIF1<0，則SKIPIF1<0．27．（2022?新高考Ⅱ）若SKIPIF1<0，則SKIPIF1<0SKIPIF1<0A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<028．（2021?新高考Ⅰ）若SKIPIF1<0，則SKIPIF1<0SKIPIF1<0A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<029．（2021?甲卷（文））若SKIPIF1<0，SKIPIF1<0，則SKIPIF1<0SKIPIF1<0A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<030．（2022?上海）若SKIPIF1<0，則SKIPIF1<0．31．（2021?乙卷（文））SKIPIF1<0SKIPIF1<0A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<032．（2022?浙江）若SKIPIF1<0，SKIPIF1<0，則SKIPIF1<0．知識(shí)點(diǎn)6：SKIPIF1<0與SKIPIF1<0的取值與范圍問(wèn)題33．（2022?甲卷（理））設(shè)函數(shù)SKIPIF1<0在區(qū)間SKIPIF1<0恰有三個(gè)極值點(diǎn)、兩個(gè)零點(diǎn)，則SKIPIF1<0的取值范圍是SKIPIF1<0SKIPIF1<0A．SKIPIF1<0，SKIPIF1<0 B．SKIPIF1<0，SKIPIF1<0 C．SKIPIF1<0，SKIPIF1<0 D．SKIPIF1<0，SKIPIF1<034．（2023?新高考Ⅰ）已知函數(shù)SKIPIF1<0在區(qū)間SKIPIF1<0，SKIPIF1<0有且僅有3個(gè)零點(diǎn)，則SKIPIF1<0的取值范圍是．35．（2022?乙卷）記函數(shù)SKIPIF1<0，SKIPIF1<0的最小正周期為SKIPIF1<0．若SKIPIF1<0，SKIPIF1<0為SKIPIF1<0的零點(diǎn)，則SKIPIF1<0的最小值為．36．（2021?北京）若點(diǎn)SKIPIF1<0關(guān)于SKIPIF1<0軸的對(duì)稱點(diǎn)為SKIPIF1<0，SKIPIF1<0，則SKIPIF1<0的一個(gè)取值為．37．（2021?上海）已知SKIPIF1<0，對(duì)任意的SKIPIF1<0，SKIPIF1<0，都存在SKIPIF1<0，SKIPIF1<0，使得SKIPIF1<0成立，則下列選項(xiàng)中，SKIPIF1<0可能的值是SKIPIF1<0SKIPIF1<0A．SKIPIF1<0 B．SK