新高考數(shù)學(xué)一輪復(fù)習(xí) 講與練第14講 三角函數(shù)的圖像和性質(zhì)（原卷版）

第14講三角函數(shù)的圖像和性質(zhì)學(xué)校____________姓名____________班級____________一、知識梳理1.用五點(diǎn)法作正弦函數(shù)和余弦函數(shù)的簡圖(1)正弦函數(shù)y＝sinx，x∈[0，2π]的圖像中，五個關(guān)鍵點(diǎn)是：(0，0)，eq\b\lc\(\rc\)(\a\vs4\al\co1(\f(π,2)，1))，(π，0)，eq\b\lc\(\rc\)(\a\vs4\al\co1(\f(3π,2)，－1))，(2π，0).(2)余弦函數(shù)y＝cosx，x∈[0，2π]的圖像中，五個關(guān)鍵點(diǎn)是：(0，1)，eq\b\lc\(\rc\)(\a\vs4\al\co1(\f(π,2)，0))，(π，－1)，eq\b\lc\(\rc\)(\a\vs4\al\co1(\f(3π,2)，0))，(2π，1).2.正弦、余弦、正切函數(shù)的圖像與性質(zhì)(下表中k∈Z)函數(shù)y＝sinxy＝cosxy＝tanx圖像定義域RR{xeq\b\lc\|(\a\vs4\al\co1(x∈R，且))x≠kπ＋eq\f(π,2)}值域[－1，1][－1，1]R最小正周期2π2ππ奇偶性奇函數(shù)偶函數(shù)奇函數(shù)遞增區(qū)間eq\b\lc\[(\a\vs4\al\co1(2kπ－\f(π,2)，))eq\b\lc\\rc\](\a\vs4\al\co1(2kπ＋\f(π,2)))[2kπ－π，2kπ]eq\b\lc\((\a\vs4\al\co1(kπ－\f(π,2)，))eq\b\lc\\rc\)(\a\vs4\al\co1(kπ＋\f(π,2)))遞減區(qū)間eq\b\lc\[(\a\vs4\al\co1(2kπ＋\f(π,2)，))eq\b\lc\\rc\](\a\vs4\al\co1(2kπ＋\f(3π,2)))[2kπ，2kπ＋π]無對稱中心(kπ，0)eq\b\lc\(\rc\)(\a\vs4\al\co1(kπ＋\f(π,2)，0))eq\b\lc\(\rc\)(\a\vs4\al\co1(\f(kπ,2)，0))對稱軸方程x＝kπ＋eq\f(π,2)x＝kπ無考點(diǎn)和典型例題1、三角函數(shù)的定義域和值域【典例1-1】（2022·河北邯鄲·二模）函數(shù)SKIPIF1<0在SKIPIF1<0上的值域?yàn)椋?/p>

）A．SKIPIF1<0 B．SKIPIF1<0C．SKIPIF1<0 D．SKIPIF1<0【典例1-2】（2022·遼寧·東港市第二中學(xué)高一期中）函數(shù)SKIPIF1<0，若SKIPIF1<0，則SKIPIF1<0的最小值是（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<0【典例1-3】（2022·全國·模擬預(yù)測（文））已知函數(shù)SKIPIF1<0，則下列結(jié)論中正確的是（

）A．函數(shù)SKIPIF1<0的最小正周期為SKIPIF1<0 B．SKIPIF1<0時SKIPIF1<0取得最小值C．SKIPIF1<0關(guān)于SKIPIF1<0對稱 D．SKIPIF1<0時SKIPIF1<0取得最大值【典例1-4】（2022·陜西·西北工業(yè)大學(xué)附屬中學(xué)模擬預(yù)測（理））已知不等式SKIPIF1<0對SKIPIF1<0恒成立，則m的最小值為（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<0【典例1-5】（2022·重慶八中高三階段練習(xí)）函數(shù)SKIPIF1<0在SKIPIF1<0上的值域是SKIPIF1<0，則SKIPIF1<0的取值范圍是（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<02、三角函數(shù)的周期性、奇偶性、對稱性【典例2-1】（2022·山東威?！と＃┘褐瘮?shù)SKIPIF1<0為偶函數(shù)，則SKIPIF1<0(

)A．0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<0【典例2-2】（2022·天津和平·三模）函數(shù)SKIPIF1<0，將函數(shù)SKIPIF1<0的圖象向左平移SKIPIF1<0個單位長度，得到函數(shù)SKIPIF1<0的圖象，若SKIPIF1<0為偶函數(shù)，則SKIPIF1<0的最小值是（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<0【典例2-3】（2022·內(nèi)蒙古赤峰·三模（文））已知函數(shù)SKIPIF1<0的圖像經(jīng)過點(diǎn)SKIPIF1<0，則SKIPIF1<0的最小正周期為（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<0【典例2-4】（2022·陜西西安·一模（理））若函數(shù)SKIPIF1<0的最小正周期為SKIPIF1<0，則SKIPIF1<0是（

）A．奇函數(shù) B．偶函數(shù)C．非奇非偶函數(shù) D．是奇函數(shù)也是偶函數(shù)【典例2-5】（2022·新疆克拉瑪依·三模（文））已知函數(shù)SKIPIF1<0的最小值周期為SKIPIF1<0，將SKIPIF1<0的圖象向右平移SKIPIF1<0個單位長度，所得圖象關(guān)于SKIPIF1<0軸對稱，則SKIPIF1<0的一個值是（

）A．SKIPIF1<0 B．SKIPIF1<0C．SKIPIF1<0 D．SKIPIF1<03、三角函數(shù)的單調(diào)性【典例3-1】（2022·天津南開·三模）將函數(shù)SKIPIF1<0的圖象向左平移SKIPIF1<0個單位，得到函數(shù)SKIPIF1<0的圖象，若函數(shù)SKIPIF1<0在區(qū)間SKIPIF1<0上單調(diào)遞增，則SKIPIF1<0的值可能為（

）A．SKIPIF1<0 B．SKIPIF1<0 C．3 D．4【典例3-2】（2022·湖北·荊州中學(xué)模擬預(yù)測）已知函數(shù)SKIPIF1<0在SKIPIF1<0單調(diào)遞減，則SKIPIF1<0的最大值為（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<0【典例3-3】（2022·全國·模擬預(yù)測（文））將函數(shù)SKIPIF1<0的圖象向左平移SKIPIF1<0個單位長度，再保持所有點(diǎn)的縱坐標(biāo)不變，橫坐標(biāo)縮短為原來的SKIPIF1<0倍，得到函數(shù)SKIPIF1<0的圖象，則使得SKIPIF1<0單調(diào)遞增的一個區(qū)間是（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<0【典例3-4】（2022·安徽·合肥一中模擬預(yù)測（文））下列函數(shù)中，既是偶函數(shù)，又在區(qū)間SKIPIF1<0內(nèi)是增函數(shù)的為（

）A．SKIPIF1<0 B．SKIPIF1<0C．SKIPIF1<0 D．SKIPIF1<0【典例3-5】（2022·全國·高三專題練習(xí)）將函數(shù)SKIPIF1<0圖象上所有點(diǎn)的橫坐標(biāo)縮短到原來的SKIPIF1<0倍SKIPIF1<0縱坐標(biāo)不變SKIPIF1<0，再向左平移SKIPIF1<0個單位長度，得到函數(shù)SKIPIF1<0的圖象，若SKIPIF1<0在SKIPIF1<0上單調(diào)遞減，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【典例3-6】（2022·河北·石家莊二中模擬預(yù)測）已知函數(shù)SKIPIF1<0.(1)求函數(shù)SKIPIF1<0在SKIP