f(x)=2αcos^x+bsinxcosx-根号(3)/2,且f(0)=根号(3)/2,f(π/4)=1/2 (1)最小正周期 (2)单点递减区间
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f(x)=2αcos^x+bsinxcosx-根号(3)/2,且f(0)=根号(3)/2,f(π/4)=1/2 (1)最小正周期 (2)单点递减区间, (3)函数f(x)的图像经过怎样的平移才能使所得图像对应的函数成为奇函数
(1)解析:∵f(x)=2α(cosx)^2+bsinxcosx-√3/2,且f(0)= √3/2,f(π/4)=1/2
f(0)=2α-√3/2=√3/2==>a=√3/2,f(π/4)= α+b/2-√3/2=1/2==>b=1
∴f(x)= √3(cosx)^2+sinxcosx-√3/2=√3/2cos2x+1/2sin2x=sin(2x+π/3)
∴最小正周期为T=π
(2)解析:2kπ+π/2<=2x+π/3<=2kπ+3π/2==>kπ+π/12<=x<=kπ+7π/12
∴单调递减区间为kπ+π/12<=x<=kπ+7π/12
(3)解析:∵f(x)=sin(2x+π/3)=sin[2(x+π/6)]
将函数f(x)的图像向右平移π/6个单位,能使所得图像对应的函数成为奇函数
(1)解析:∵f(x)=2α(cosx)^2+bsinxcosx-√3/2,且f(0)= √3/2,f(π/4)=1/2
f(0)=2α-√3/2=√3/2==>a=√3/2,f(π/4)= α+b/2-√3/2=1/2==>b=1
∴f(x)= √3(cosx)^2+sinxcosx-√3/2=√3/2cos2x+1/2sin2x=sin(2x+π/3)
∴最小正周期为T=π
(2)解析:2kπ+π/2<=2x+π/3<=2kπ+3π/2==>kπ+π/12<=x<=kπ+7π/12
∴单调递减区间为kπ+π/12<=x<=kπ+7π/12
(3)解析:∵f(x)=sin(2x+π/3)=sin[2(x+π/6)]
将函数f(x)的图像向右平移π/6个单位,能使所得图像对应的函数成为奇函数
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