新高考數(shù)學(xué)一輪復(fù)習(xí)第4章 第04講 簡(jiǎn)單的三角恒等變換 精講+精練（學(xué)生版）

第04講簡(jiǎn)單的三角恒等變換(精講+精練）目錄第一部分：知識(shí)點(diǎn)精準(zhǔn)記憶第二部分：課前自我評(píng)估測(cè)試第三部分：典型例題剖析高頻考點(diǎn)一：三角函數(shù)式的化簡(jiǎn)高頻考點(diǎn)二：三角函數(shù)求值問題角度1：給角求值型角度2：給值求值型角度3：給值求角型高頻考點(diǎn)三：三角恒等變換的應(yīng)用第四部分：高考真題感悟第五部分：第04講簡(jiǎn)單的三角恒等變換（精練）第一部分：知識(shí)點(diǎn)精準(zhǔn)記憶第一部分：知識(shí)點(diǎn)精準(zhǔn)記憶1、半角公式（1）SKIPIF1<0.（2）SKIPIF1<0.（3）SKIPIF1<0.2、萬能公式（拓展視野）（1）SKIPIF1<0（2）SKIPIF1<0（3）SKIPIF1<0其中SKIPIF1<03、和差化積公式（拓展視野）SKIPIF1<04、積化和差公式（拓展視野）SKIPIF1<0SKIPIF1<0SKIPIF1<0SKIPIF1<0第二部分：課前自我評(píng)估測(cè)試第二部分：課前自我評(píng)估測(cè)試1．（2022·全國(guó)·高二課時(shí)練習(xí)）若cosα＝SKIPIF1<0，α∈(0，π)，則cosSKIPIF1<0的值為（

）A．SKIPIF1<0 B．－SKIPIF1<0 C．SKIPIF1<0 D．－SKIPIF1<02．（2022·全國(guó)·高一專題練習(xí)）SKIPIF1<0化簡(jiǎn)的結(jié)果可以是（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<03．（2022·全國(guó)·高一課時(shí)練習(xí)）SKIPIF1<0的值為（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<04．（2022·河北·張家口市宣化第一中學(xué)高一階段練習(xí)）已知SKIPIF1<0為銳角，且SKIPIF1<0，則SKIPIF1<0的值為（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<05．（2022·黑龍江·哈爾濱市第三十二中學(xué)校高一期中）若SKIPIF1<0則SKIPIF1<0的值是（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<06．（2022·全國(guó)·高三專題練習(xí)（文））已知SKIPIF1<0，SKIPIF1<0，則SKIPIF1<0（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<0第三部分：典型例題剖析第三部分：典型例題剖析高頻考點(diǎn)一：三角函數(shù)式的化簡(jiǎn)例題1．（2022·陜西·榆林市第一中學(xué)高一期中（文））化簡(jiǎn)計(jì)算：SKIPIF1<0___________．例題2．（2022·湖南·模擬預(yù)測(cè)）SKIPIF1<0___________．題型歸類練1．（2022·湖北·沙市中學(xué)高一期中）化簡(jiǎn)：SKIPIF1<0（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<02．（2022·海南海口·模擬預(yù)測(cè)）若SKIPIF1<0，則SKIPIF1<0的值為（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．3高頻考點(diǎn)二：三角函數(shù)求值問題角度1：給角求值型例題1．（2022·江蘇·吳縣中學(xué)高一期中）計(jì)算：SKIPIF1<0SKIPIF1<0（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<0例題2．（2022·山西朔州·高一期末）SKIPIF1<0________.例題3．（2022·陜西·涇陽(yáng)縣教育局教學(xué)研究室高一期中）計(jì)算求值：(1)計(jì)算SKIPIF1<0的值；(2)已知SKIPIF1<0、SKIPIF1<0均為銳角，SKIPIF1<0，SKIPIF1<0，求SKIPIF1<0的值．角度1題型歸類練1．（2022·四川·石室中學(xué)模擬預(yù)測(cè)（文））SKIPIF1<0的值為（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<02．（多選）（2022·全國(guó)·高三專題練習(xí)）下列選下選項(xiàng)中，值為SKIPIF1<0的是（

）A．SKIPIF1<0 B．SKIPIF1<0C．SKIPIF1<0 D．SKIPIF1<03．（2022·全國(guó)·高三專題練習(xí)）SKIPIF1<0___________.角度2：給值求值型例題1．（2022·河南商丘·三模（文））已知SKIPIF1<0，則SKIPIF1<0（

）A．3 B．SKIPIF1<0 C．SKIPIF1<0 D．-3例題2．（2022·北京八中高一期中）設(shè)SKIPIF1<0為銳角，若SKIPIF1<0，則SKIPIF1<0的值為________，SKIPIF1<0的值為________.例題3．（2022·北京市第十九中學(xué)高一期中）已知SKIPIF1<0，SKIPIF1<0.(1)求SKIPIF1<0的值；(2)求SKIPIF1<0的值.角度2題型歸類練1．（2022·黑龍江·哈師大附中三模（文））已知SKIPIF1<0，SKIPIF1<0，則SKIPIF1<0（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<02．（2022·遼寧·建平縣實(shí)驗(yàn)中學(xué)模擬預(yù)測(cè)）已知SKIPIF1<0，則SKIPIF1<0（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<03．（2022·陜西·長(zhǎng)安一中高一期中）已知SKIPIF1<0，且SKIPIF1<0，則SKIPIF1<0________．4．（2022·四川·射洪中學(xué)高一階段練習(xí)）已知SKIPIF1<0，則SKIPIF1<0的值為___________.5．（2022·北京市第二十五中學(xué)高一期中）已知SKIPIF1<0，SKIPIF1<0，且SKIPIF1<0．(1)求SKIPIF1<0的值；(2)求SKIPIF1<0的值；(3)求SKIPIF1<0的值．角度3：給值求角型例題1．（2022·陜西·西安中學(xué)高一期中）若SKIPIF1<0，則角SKIPIF1<0的值為（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<0例題2．（2022·江蘇·蘇州市蘇州高新區(qū)第一中學(xué)高一期中）設(shè)SKIPIF1<0，且SKIPIF1<0，則SKIPIF1<0（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<0例題3．（2022·江蘇鹽城·高一期中）已知SKIPIF1<0(1)求SKIPIF1<0的值；(2)已知SKIPIF1<0，SKIPIF1<0，SKIPIF1<0，求SKIPIF1<0的值.角度3題型歸類練1．（2022·吉林·延邊州教育學(xué)院一模（理））若SKIPIF1<0，SKIPIF1<0，且SKIPIF1<0，SKIPIF1<0，則SKIPIF1<0（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<02．（2022·江蘇·金陵中學(xué)高一期中）已知SKIPIF1<0，SKIPIF1<0，SKIPIF1<0，則SKIPIF1<0（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<03．（2022·河南·南陽(yáng)中學(xué)高三階段練習(xí)（文））已知SKIPIF1<0，且SKIPIF1<0，求SKIPIF1<0的值為_____．4．（2022·江蘇·高一期中）已知SKIPIF1<0，SKIPIF1<0，SKIPIF1<0，SKIPIF1<0，則SKIPIF1<0________．5．（2022·上海市大同中學(xué)高三開學(xué)考試）若SKIPIF1<0，且SKIPIF1<0，則SKIPIF1<0的值為___________.6．（2022·湖南·株洲二中高一階段練習(xí)）已知SKIPIF1<0.(1)若SKIPIF1<0，求SKIPIF1<0的值；(2)若SKIPIF1<0，SKIPIF1<0且SKIPIF1<0，求SKIPIF1<0的值.高頻考點(diǎn)三：三角恒等變換的應(yīng)用例題1．（2022·江蘇省沙溪高級(jí)中學(xué)高一期中）已知SKIPIF1<0(1)求SKIPIF1<0的值；(2)若銳角SKIPIF1<0滿足SKIPIF1<0，求SKIPIF1<0的值.例題2．（2022·河南洛陽(yáng)·高二期中（文））某同學(xué)在一次研究性學(xué)習(xí)中發(fā)現(xiàn)，以下四個(gè)式子的值等于同一個(gè)常數(shù)：①SKIPIF1<0；②SKIPIF1<0；③SKIPIF1<0；④SKIPIF1<0.(1)試從上述四個(gè)式子中選擇一個(gè)，求出這個(gè)常數(shù)；(2)根據(jù)（1）的計(jì)算結(jié)果，將該同學(xué)的發(fā)現(xiàn)推廣為三角恒等式，并證明你的結(jié)論.例題3．（2022·江西·南昌十中高一期中）如圖，圓心角為SKIPIF1<0的扇形SKIPIF1<0的半徑為2，點(diǎn)C是弧AB上一點(diǎn)，作這個(gè)扇形的內(nèi)接矩形SKIPIF1<0．(1)求扇形SKIPIF1<0的周長(zhǎng)；(2)當(dāng)點(diǎn)C在什么位置時(shí)，矩形SKIPIF1<0的面積最大？并求出面積的最大值．題型歸類練1．（2022·浙江嘉興·二模）設(shè)函數(shù)SKIPIF1<0SKIPIF1<0.(1)求函數(shù)SKIPIF1<0的最小正周期及其對(duì)稱中心；(2)求函數(shù)SKIPIF1<0在SKIPIF1<0上的值域.2．（2022·全國(guó)·高三專題練習(xí)）已知函數(shù)SKIPIF1<0，若SKIPIF1<0，求SKIPIF1<0的值.3．（2022·貴州·凱里一中高一開學(xué)考試）已知扇形SKIPIF1<0（如圖所示），圓心角SKIPIF1<0，半徑SKIPIF1<0，在弧SKIPIF1<0上取一點(diǎn)P，作扇形SKIPIF1<0的內(nèi)接矩形SKIPIF1<0，記SKIPIF1<0，矩形SKIPIF1<0的面積為y.(1)寫出y與x的函數(shù)關(guān)系式，并化簡(jiǎn)；(2)求矩形SKIPIF1<0面積的最大值，并求此時(shí)x的取值.第四部分：高考真題感悟第四部分：高考真題感悟1．（2021·北京·高考真題）函數(shù)SKIPIF1<0是A．奇函數(shù)，且最大值為2 B．偶函數(shù)，且最大值為2C．奇函數(shù)，且最大值為SKIPIF1<0 D．偶函數(shù)，且最大值為SKIPIF1<02．（2021·全國(guó)·高考真題（文））SKIPIF1<0（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<03．（2021·全國(guó)·高考真題（文））若SKIPIF1<0，則SKIPIF1<0（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<04．（2021·全國(guó)·高考真題（文））函數(shù)SKIPIF1<0的最小正周期和最大值分別是（

）A．SKIPIF1<0和SKIPIF1<0 B．SKIPIF1<0和2 C．SKIPIF1<0和SKIPIF1<0 D．SKIPIF1<0和25．（2021·全國(guó)·高考真題）若SKIPIF1<0，則SKIPIF1<0（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<06．（2021·浙江·高考真題）設(shè)函數(shù)SKIPIF1<0.（1）求函數(shù)SKIPIF1<0的最小正周期；（2）求函數(shù)SKIPIF1<0在SKIPIF1<0上的最大值.第五部分：第五部分：第04講簡(jiǎn)單的三角恒等變換（精練）一、單選題1．（2022·江蘇·蘇州外國(guó)語(yǔ)學(xué)校高一期中）若SKIPIF1<0，且SKIPIF1<0，則SKIPIF1<0的值為（

）A．SKIPIF1<0 B．SKIPIF1<0C．SKIPIF1<0 D．SKIPIF1<02．（2022·江西·臨川一中高三期中（文））已知SKIPIF1<0，則SKIPIF1<0（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<03．（2022·廣東汕頭·二模）若SKIPIF1<0，則實(shí)數(shù)SKIPIF1<0的值為（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<04．（2022·山西運(yùn)城·高一階段練習(xí)）已知SKIPIF1<0，則SKIPIF1<0（

）A．SKIPIF1<0 B．SKIPIF1<0 C．1 D．SKIPIF1<05．（2022·江蘇·東?？h教育局教研室高一期中）函數(shù)SKIPIF1<0，SKIPIF1<0，則SKIPIF1<0的最大值為（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<06．（2022·河南·模擬預(yù)測(cè)（理））已知SKIPIF1<0，則SKIPIF1<0（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<07．（2022·廣東茂名·模擬預(yù)測(cè)）已知SKIPIF1<0，則SKIPIF1<0(

)A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<08．（2022·全國(guó)·高三專題練習(xí)）已知SKIPIF1<0