新高考數(shù)學二輪復習易錯點05 三角變換及三角函數(shù)的性質(zhì)（原卷版）

易錯點05三角變換及三角函數(shù)的性質(zhì)易錯題【01】忽略角的范圍限制利用SKIPIF1<0求值一般要涉及到開方運算,此時要注意利用角的范圍判斷三角函數(shù)值的正負；根據(jù)三角函數(shù)值求角,一般是先求出該角的某一個三角函數(shù)值,再確定角的范圍,確定角的范圍時不僅要看已知條件中角的范圍,還要挖掘隱含條件,根據(jù)三角函數(shù)值的符號及大小縮小角的范圍易錯題【02】不能全面理解三角函數(shù)性質(zhì)致誤本易錯點主要包含以下幾個問題：(1)求三角函數(shù)值域忽略定義域的限制；(2)確定三角函數(shù)的最小正周期,忽略三角變換的等價性；(3)求復合函數(shù)的單調(diào)性忽略對內(nèi)函數(shù)單調(diào)性的判斷.易錯題【03】對平移理解不準確致誤三角函數(shù)圖象的左右平移是自變量x發(fā)生變化,如ωx→ωx±φ(φ>0)這個變化的實質(zhì)是x→x±eq\f(φ,ω),所以平移的距離并不一定是φ.易錯題【04】忽視弦函數(shù)的有界性在求與SKIPIF1<0,SKIPIF1<0有關的值域與范圍是要注意SKIPIF1<0.易錯題【05】用零點確定SKIPIF1<0的SKIPIF1<0,忽略圖象的升降確定φ值時,往往以尋找“五點法”中的特殊點作為突破口．具體如下：“第一點”(即圖象上升時與x軸的交點)為ωx＋φ＝0；“第二點”(即圖象的“峰點”)為ωx＋φ＝eq\f(π,2)；“第三點”(即圖象下降時與x軸的交點)為ωx＋φ＝π；“第四點”(即圖象的“谷點”)為ωx＋φ＝eq\f(3π,2)；“第五點”為ωx＋φ＝2π. 01已知sinα＝eq\f(\r(5),5),sinβ＝eq\f(\r(10),10),且α,β為銳角,則α＋β＝________.1.(2022屆福建省永安市高三10月月考)已知SKIPIF1<0的終邊在第四象限,若SKIPIF1<0,則SKIPIF1<0()A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<02.已知SKIPIF1<0為銳角,SKIPIF1<0,SKIPIF1<0,則SKIPIF1<0的值為()A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<0 02函數(shù)SKIPIF1<0得最小正周期為.1．求函數(shù)SKIPIF1<0的值域.2.(2022屆山東省青島市高三上學期期中)若函數(shù)SKIPIF1<0的最小正周期為SKIPIF1<0,則函數(shù)SKIPIF1<0在SKIPIF1<0上的值域為_______． 03(2022全國乙卷理T7)把函數(shù)SKIPIF1<0圖像上所有點的橫坐標縮短到原來的SKIPIF1<0倍,縱坐標不變,再把所得曲線向右平移SKIPIF1<0個單位長度,得到函數(shù)SKIPIF1<0的圖像,則SKIPIF1<0SKIPIF1<0A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<01．要得到y(tǒng)＝sin(－3x)的圖象,需將y＝eq\f(\r(2),2)(cos3x－sin3x)的圖象A．向右平移eq\f(π,4)個單位 B．向左平移eq\f(π,4)個單位C．向右平移eq\f(π,12)個單位 D．向左平移eq\f(π,12)個單位2．(2022屆海南省華僑中學高三11月月考)將函數(shù)y＝f(x)的圖象向左平移SKIPIF1<0個單位長度,再把所得圖象上所有點的橫坐標伸長到原來的2倍得到y(tǒng)＝sinSKIPIF1<0的圖象,則f(x)＝()A．sinSKIPIF1<0 B．sinSKIPIF1<0 C．sinSKIPIF1<0 D．sinSKIPIF1<0 04已知SKIPIF1<0,則SKIPIF1<0的取值范圍是.1.(2022屆甘肅省部分名校年高三上學期月考)已知函數(shù)SKIPIF1<0．若關于x的方程SKIPIF1<0在SKIPIF1<0上有解,則實數(shù)m的取值范圍是()A．SKIPIF1<0 B．SKIPIF1<0C．SKIPIF1<0 D．SKIPIF1<02．(2022屆四川省綿陽高三上學期一診)已知SKIPIF1<0,則SKIPIF1<0的最大值為____________ 05函數(shù)f(x)＝sin(ωx＋φ)(x∈R,ω>0,|φ|<SKIPIF1<0)的部分圖象如圖所示,則SKIPIF1<0.1.已知函數(shù)SKIPIF1<0(SKIPIF1<0,SKIPIF1<0)的部分圖象如圖所示,將SKIPIF1<0圖象進行怎樣的平移變換后得到的圖象對應的函數(shù)SKIPIF1<0為奇函數(shù)()A．向左平移SKIPIF1<0個單位長度 B．向右平移SKIPIF1<0個單位長度C．向左平移SKIPIF1<0個單位長度 D．向右平移SKIPIF1<0個單位長度2.(2022屆重慶市八中高三上學期月考)(多選題)函數(shù)SKIPIF1<0的圖象如圖所示,則關于函數(shù)SKIPIF1<0下列結論中正確的是()A．SKIPIF1<0 B．SKIPIF1<0C．對稱軸為SKIPIF1<0 D．對稱中心為SKIPIF1<0錯1．(2022屆河北省衡水市冀州區(qū)高三上學期期中)已知SKIPIF1<0且SKIPIF1<0,若SKIPIF1<0,則SKIPIF1<0()A．SKIPIF1<0或SKIPIF1<0 B．SKIPIF1<0或1 C．1 D．SKIPIF1<02．若SKIPIF1<0,且SKIPIF1<0,則SKIPIF1<0()A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<03．設銳角SKIPIF1<0的內(nèi)角SKIPIF1<0,SKIPIF1<0,SKIPIF1<0的對邊分別為SKIPIF1<0,SKIPIF1<0,SKIPIF1<0,若SKIPIF1<0,則SKIPIF1<0的取值范圍是()A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<04．(2021屆安徽省合肥市高三下學期第二次教學質(zhì)量檢測)在SKIPIF1<0ABC中,已知SKIPIF1<0,SKIPIF1<0,則cosC=()A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0或SKIPIF1<0 D．SKIPIF1<05．(2022屆北京師范大學附屬中學高三上學期期中)將SKIPIF1<0的圖象向右平移SKIPIF1<0個單位,則所得圖象的函數(shù)解析式為()A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<06．(2021屆湘豫名校名校高三5月聯(lián)考)已知函數(shù)SKIPIF1<0的圖象沿SKIPIF1<0軸向右平移SKIPIF1<0個單位長度后得到函數(shù)SKIPIF1<0的圖象,則SKIPIF1<0的一個對稱中心為()A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<07．(2022屆四川省成都高三上學期階段性檢)函數(shù)SKIPIF1<0,(其中SKIPIF1<0,SKIPIF1<0,SKIPIF1<0)其圖象如圖所示,為了得到SKIPIF1<0的圖象,可以將SKIPIF1<0的圖象()A．向右平移SKIPIF1<0個單位長度 B．向右平移SKIPIF1<0個單位長度C．向左平移SKIPIF1<0個單位長度 D．向左平移SKIPIF1<0個單位長度8．(2022屆江蘇省南通市高三上學期期中)已知函數(shù)SKIPIF1<0(SKIPIF1<0,SKIPIF1<0,SKIPIF1<0)的部分圖象如圖所示,將函數(shù)SKIPIF1<0的圖象向左平移SKIPIF1<0個單位長度后得到SKIPIF1<0的圖象,則下列說法正確的是()A．SKIPIF1<0B．SKIPIF1<0C．函數(shù)SKIPIF1<0為奇函數(shù)D．函數(shù)SKIPIF1<0在區(qū)間SKIPIF1<0上單調(diào)遞減9．(2022屆安徽省合肥市高三上學期11月月)(多選題)已知函數(shù)SKIPIF1<0,則下列結論不正確的是()A．函數(shù)SKIPIF1<0的最小正周期是SKIPIF1<0 B．函數(shù)SKIPIF1<0在區(qū)間SKIPIF1<0上是減函數(shù)C．函數(shù)SKIPIF1<0