專題突破練7三角函數(shù)的圖象與性質123456789101112主干知識達標練13141516B12345678910111213141516A1234567891011121314151612345678910111213141516A12345678910111213141516解析

如圖,①和②面積相等,故陰影部分的面積即為矩形ABCD的面積,可得AB=3,設函數(shù)f(x)的最小正周期為T,則AD=T,由題意得3T=6π,解得T=2π,12345678910111213141516D1234567891011121314151612345678910111213141516A.①②

B.③④

C.①②④ D.①③④C123456789101112131415161234567891011121314151612345678910111213141516ABD12345678910111213141516123456789101112131415161234567891011121314151612345678910111213141516ABD123456789101112131415161234567891011121314151612345678910111213141516AC123456789101112131415161234567891011121314151612345678910111213141516sinx1234567891011121314151610.(5分)(2024河南平頂山模擬)寫出一個同時滿足下列三個條件的函數(shù)f(x)的解析式:

.

①f(x)=-f(x+2);②f(x+1)=f(1-x);③f(x)的導數(shù)為f'(x)且f'(x)=f'(-x).解析

由①得f(x+4)=f(x),所以函數(shù)f(x)的周期為4.由②得f(x)的圖象關于直線x=1對稱.由③得f(x)的圖象關于點(0,c)對稱,c為常數(shù).12345678910111213141516關鍵能力提升練11.(2024陜西西安二模)正弦波是頻率成分非常單一的信號,其波形是數(shù)學上的正弦曲線,任何復雜信號,如光譜信號、聲音信號等,都可由多個不同的正弦波復合而成.現(xiàn)已知某復合信號I(x)由三個振幅、頻率相同的正弦波f(x),g(x),h(x)疊加而成,即I(x)=f(x)+g(x)+h(x),設f(x)=Asin(ωx+φ),g(x)=Asin(ωx+α),h(x)=Asin(ωx+β)(A>0,ω>0,|φ|<,α,β∈(0,π)),若圖中所示為f(x)的部分圖象,則下列描述正確的是(

)D123456789101112131415161234567891011121314151612345678910111213141516BCD123456789101112131415161234567891011121314151613.(多選題)(2024河北秦皇島三模)已知函數(shù)f(x)=2|sinx|cosx,則(

)A.f(x)是偶函數(shù)B.f(x)是周期為π的周期函數(shù)AD解析

顯然f(x)的定義域是R.因為f(-x)=2|sin(-x)|cos(-x)=2|sin

x|cos

x=f(x),所以f(x)是偶函數(shù),故A正確;易知f(x+π)=2|sin(x+π)|cos(x+π)=2-|sin

x|cos

x≠f(x),故B錯誤;12345678910111213141516123456789101112131415161234567891011121314151612345678910111213141516123456789101112131415161234567891011121314151612345678910111213141516核心素養(yǎng)創(chuàng)新練16.(2024海南學業(yè)水平診斷)若函數(shù)y=2sinωx與y=2cosωx的圖象的任意連續(xù)三個交點均構成鈍角三角形,則正實數(shù)ω的取值范圍是