新高考數(shù)學一輪復習3.4.1 三角函數(shù)的性質(zhì)（1）（精練）（基礎版）（原卷版）

3.4.1三角函數(shù)的性質(zhì)（1）（精練）（基礎版）題組一題組一周期1．（2022·廣西南寧）下列四個函數(shù)，最小正周期是SKIPIF1<0的是（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<02.（2021年湖南）下列函數(shù)中，周期為2π的奇函數(shù)為()A．y＝sineq\f(x,2)coseq\f(x,2)B．y＝sin2xC．y＝tan2xD．y＝sin2x＋cos2x3．（2022·江西景德鎮(zhèn)）函數(shù)SKIPIF1<0的最小正周期為（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<04．（2022·寧夏·青銅峽市寧朔中學）函數(shù)SKIPIF1<0的最小正周期為________.5．（2022·陜西·西安市臨潼區(qū)鐵路中學）已知函數(shù)f(x)＝sin(ωx＋SKIPIF1<0)(ω>0)的最小正周期為π，則ω＝____.6．（2022·全國·高三專題練習）求下列三角函數(shù)的周期：(1)y＝3sinx，x∈R；

(2)y＝cos2x，x∈R；(3)y＝sinSKIPIF1<0，x∈R；

(4)y＝|cosx|，x∈R.7（2021·上海·高三專題練習）求下列函數(shù)的周期：（1）SKIPIF1<0；

（2）SKIPIF1<0.題組二題組二對稱性1．（2022·全國·單元測試）函數(shù)SKIPIF1<0圖象的對稱中心的坐標為（

）A．SKIPIF1<0 B．SKIPIF1<0C．SKIPIF1<0 D．SKIPIF1<02．（2022·安徽）“SKIPIF1<0”是“函數(shù)SKIPIF1<0的圖象關于SKIPIF1<0對稱”的（

）A．充分不必要條件 B．必要不充分條件C．充分必要條件 D．既不充分也不必要條件3．（2021·青海西寧）已知函數(shù)SKIPIF1<0的圖象過點SKIPIF1<0，則SKIPIF1<0圖象的一個對稱中心為（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<04．（2022·浙江金華）下列函數(shù)中，關于直線SKIPIF1<0對稱的是（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<05（2022·全國·單元測試）函數(shù)SKIPIF1<0的圖像（

）A．關于點SKIPIF1<0對稱 B．關于點SKIPIF1<0對稱C．關于直線SKIPIF1<0對稱 D．關于直線SKIPIF1<0對稱6．（2022·河北?。╆P于SKIPIF1<0有下列結論:①函數(shù)的最小正周期為SKIPIF1<0；

②表達式可改寫成SKIPIF1<0；③函數(shù)的圖象關于點SKIPIF1<0對稱；

④函數(shù)的圖象關于直線SKIPIF1<0對稱.其中錯誤的結論是()A．①② B．①③ C．④ D．②③7．（2021·北京市）最小正周期為SKIPIF1<0，且圖象關于直線SKIPIF1<0對稱的一個函數(shù)是（）A．SKIPIF1<0 B．SKIPIF1<0C．SKIPIF1<0 D．SKIPIF1<08．（2022·江西·南昌十五中）若函數(shù)SKIPIF1<0的圖象與SKIPIF1<0的圖象都關于直線SKIPIF1<0對稱，則SKIPIF1<0的最小值為（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<0題組三題組三奇偶性1．（2022·江西）下列函數(shù)中，既不是奇函數(shù)也不是偶函數(shù)的是（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<02．（2022·全國·高二課時練習）函數(shù)SKIPIF1<0是（

）A．周期為SKIPIF1<0的奇函數(shù) B．周期為SKIPIF1<0的偶函數(shù)C．周期為SKIPIF1<0的奇函數(shù) D．周期為SKIPIF1<0的偶函數(shù)3．（2021·全國·課時練習）下列函數(shù)中，最小正周期是SKIPIF1<0且是奇函數(shù)的是（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<04．（2022·陜西·西安市臨潼區(qū)鐵路中學）下列函數(shù)中為周期是SKIPIF1<0的偶函數(shù)是（

）A．SKIPIF1<0 B．SKIPIF1<0C．SKIPIF1<0 D．SKIPIF1<05．（2022·全國·高三專題練習）下列函數(shù)中，周期為SKIPIF1<0的奇函數(shù)為（

）．A．SKIPIF1<0 B．SKIPIF1<0C．SKIPIF1<0 D．SKIPIF1<06．（2022·新疆昌吉）已知函數(shù)SKIPIF1<0，則下列關于函數(shù)SKIPIF1<0的描述錯誤的是（

）A．奇函數(shù) B．最小正周期為SKIPIF1<0C．其圖象關于點SKIPIF1<0對稱 D．其圖象關于直線SKIPIF1<0對稱7．（2022·全國·課時練習）下列函數(shù)中，其圖像關于原點對稱的是（

）．A．SKIPIF1<0 B．SKIPIF1<0C．SKIPIF1<0 D．SKIPIF1<08．（2021·全國·課時練習）下列函數(shù)具有奇偶性的是（

）A．SKIPIF1<0 B．SKIPIF1<0C．SKIPIF1<0 D．SKIPIF1<09．（2022·河南）“函數(shù)f(x)=sin2x+(a2-1)cosx為奇函數(shù)”是“a=1”的（

）A．充分不必要條件 B．必要不充分條件C．充要條件 D．既不充分也不必要條件10．（2022·全國·專題練習）函數(shù)f（x）=SKIPIF1<0是（

）A．奇函數(shù) B．偶函數(shù)C．非奇非偶函數(shù) D．既是奇函數(shù)又是偶函數(shù)11．（2022·上海市）函數(shù)SKIPIF1<0是（

）A．最小正周期為SKIPIF1<0的奇函數(shù) B．最小正周期為SKIPIF1<0的偶函數(shù)C．最小正周期為SKIPIF1<0的奇函數(shù) D．最小正周期為SKIPIF1<0的偶函數(shù)12．（2022·全國·高三專題練習）已知函數(shù)SKIPIF1<0，則“SKIPIF1<0”是“SKIPIF1<0為偶函數(shù)”的（

）條件A．充分非必要條件 B．必要非充分條件C．充要條件 D．既非充分也非必要條件13．（2022·全國·高三專題練習）函數(shù)f(x)=SKIPIF1<0的奇偶性為（

）A．奇函數(shù)B．既是奇函數(shù)也是偶函數(shù)C．偶函數(shù)D．非奇非偶函數(shù)14．（2022·全國·高三專題練習）函數(shù)①SKIPIF1<0，②SKIPIF1<0，③SKIPIF1<0中，周期是SKIPIF1<0且為奇函數(shù)的所有函數(shù)的序號是（

）A．①② B．② C．③ D．②③15．（2022·全國·高三專題練習）已知函數(shù)SKIPIF1<0為奇函數(shù)，且存在SKIPIF1<0，使得SKIPIF1<0，則SKIPIF1<0的一個可能值為（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<016．（2022·全國·高三專題練習）使函數(shù)SKIPIF1<0為偶函數(shù)的SKIPIF1<0的一個值為（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<017．（2022·全國·高三專題練習）已知函數(shù)SKIPIF1<0．則“SKIPIF1<0是偶函數(shù)“是“SKIPIF1<0”的（

）A．充分不必要條件 B．必要不充分條件C．充分必要條件 D．既不充分也不必要條件18．（2022·全國·高三專題練習）在下列四個函數(shù)中，周期為SKIPIF1<0的偶函數(shù)為（

）A．SKIPIF1<0 B．SKIPIF1<0C．SKIPIF1<0 D．SKIPIF1<019．（2022·安徽·淮南第一中學一模（理））已知函數(shù)SKIPIF1<0，則下列說法正確的是（

）A．SKIPIF1<0為奇函數(shù) B．SKIPIF1<0為奇函數(shù)C．SKIPIF1<0為偶函數(shù) D．SKIPIF1<0為偶函數(shù)20．（2022·河南濮陽·高三開學考試（理））設SKIPIF1<0，若函數(shù)SKIPIF1<0的圖象關于原點對稱，則a的最大值為（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<0題組四題組四單調(diào)性1．（2022·內(nèi)蒙古包頭·高三期末（理））下列區(qū)間中，函數(shù)SKIPIF1<0單調(diào)遞增的區(qū)間是（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<02．（2022·全國·高三專題練習）函數(shù)SKIPIF1<0的單調(diào)遞增區(qū)間為（

）A．SKIPIF1<0，SKIPIF1<0 B．SKIPIF1<0，SKIPIF1<0C．SKIPIF1<0，SKIPIF1<0 D．SKIPIF1<0，SKIPIF1<03．（2022·河北·模擬預測）（多選）下列四個函數(shù)中，以SKIPIF1<0為周期且在SKIPIF1<0上單調(diào)遞增的偶函數(shù)有（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<04．（2022·湖南·長沙市南雅中學高三階段練習）在下列區(qū)間中，函數(shù)SKIPIF1<0單調(diào)遞增的區(qū)間是（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<05．（2022·湖北武漢·高三期末）下列四個函數(shù)中，以SKIPIF1<0為最小正周期，其在SKIPIF1<0