已知函数f(χ)=sin(2x+π/6 )+sin(2x- π/6)+cos2x+1(x∈R),
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已知函数f(χ)=sin(2x+π/6 )+sin(2x- π/6)+cos2x+1(x∈R),
已知函数f(χ)=sin(2x+π/6 )+sin(2x- π/6)+cos2x+1(x∈R),求f(χ) 的最小正周期、对称轴、对称中心、单调增区间
已知函数f(χ)=sin(2x+π/6 )+sin(2x- π/6)+cos2x+1(x∈R),求f(χ) 的最小正周期、对称轴、对称中心、单调增区间
f(x)=(√3/2)sin2x+(1/2)cos2x+(√3/2)sin2x-(1/2)cos2x+cos2x+1
=√3sin2x+cos2x+1
=2sin(2x+π/6)+1
周期T=2π/2=π
对称轴:2x+π/6=π/2+kπ,得对称轴为:x=-π/6+kπ/2,k∈Z
对称中心:2x+π/6=kπ,得对称中心为:(-π/12+kπ/2,0),k∈Z
单调增区间:
-π/2+2kπ
=√3sin2x+cos2x+1
=2sin(2x+π/6)+1
周期T=2π/2=π
对称轴:2x+π/6=π/2+kπ,得对称轴为:x=-π/6+kπ/2,k∈Z
对称中心:2x+π/6=kπ,得对称中心为:(-π/12+kπ/2,0),k∈Z
单调增区间:
-π/2+2kπ
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