函数f(x)根号三cos(π 2 π 4)的最小正周期
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函数f(x)=sin(2x+φ)+根号三cos(2x+θ)=2sin(2x+θ+π/3)的定义域为:R则f(0)=0所以:0=sin(θ+π/3),=>θ+π/3=2kπ,k∈Z即θ=2kπ-π/3所
已知:函数f(x)=2sinxcosx+2√3cos²x-√3求:(1)单调增区间和最小正周期;(2)当x∈[-π/4,π/4]时求最值.f(x)=2sinxcosx+2√3cos²
f(x)=2sinxcosx+2√3cos²x-√3=2sinxcosx+√3(2cos²x-1)=sin2x+√3cos2x=2sin(2x+π/3)最小正周期T=2π/2=π,
1、f(x)=1/2*sin(2x/3)+√3*(1+cos2x/3)/2=1/2*sin(2x/3)+√3/2*cos(2x/3)+√3/2=sin(2x/3)cosπ/3+cos(2x/3)sin
f(x)=√3cos²0.5x+sin0.5xcos0.5x=√3/2(cosx+1)+1/2sinx=sin(60°+x)+√3/2若f(x)=3/5+√3/2,即sin(60°+x)+√
f(x)=√3(cos(x/2))^2+sin(x/2)cos(x/2)=(√3/2)(cosx+1)+(1/2)sinx=sin(π/6+x)+√3/2f(x)=3/5+√3/2sin(π/6+x)
1.f(x)=cos(π/2+2X)COS(π+x)=-sin2x*(-cosx)=sin2xcosxf(-x)=sin(-2x)cos(-x)=-sin2xcosx=-f(x)∴f(x)是奇函数2.
f(x)=[sin(x+a/2)+根号3cos(x+a/2)]*cos(x+a/2)=sin(x+a/2)cos(x+a/2)+根号3cos(x+a/2)cos(x+a/2)=1/2sin(2x+a)
由函数图像性质知当2x+π/4=2kπ+π/2即x=kπ+π/8时f(x)的值最大f(x)=根号2*1+1=根号2+1当2x+π/4=2kπ+3π/2即x=kπ+5π/8时f(x)的值最小f(x)=根
由倍角公式:f(x)=sin2x-√3cos2x由辅助角公式:f(x)=2sin(2x-π/3)所以,最小正周期T=2π/2=π最大值为2
f(x)=(12)sin2x+√3cos²x=(1/2)sin2x+(√3/2)[1+cos2x]=(1/2)sin2x+(√3/2)cos2x+(√3/2)=sin(2x+π/3)+(√3
原式=sin2x/2+cosx^2根号3=1/2sin2x+根号3/2+根号3/2*cos2x=sin(2x+π/3)+根号3/2因为T=2π/ww=2所以T=π所以最小正周期为π
f(x)等于根号三cos平方x+cosxf(x)=√3cos²x+cosx=√3(cos²x+√3/3cosx)=√3(cosx+√3/6)²-√3/12因为-1≤cos
f(x)=sinxcosx+√3(cosx)^2-√3/2=(1/2)sin2x+(√3/2)cos2x=sin2xcosπ/3+cos2xsinπ/3=sin(2x+π/3)1.0
f(x)=cos(X+π/6)-cos(X-π/6)+根号三*cosx=cosxcosπ/6-sinxsinπ/6-(cosxcosπ/6+sinxsinπ/6)+√3cosx=-sinx+√3cos
f(x)=sinxcosx+√3(cosx)^2-√3/2=(1/2)sin2x+(√3/2)cos2x=sin2xcosπ/3+cos2xsinπ/3=sin(2x+π/3)
f(x)=√3cos²x+sinxcosx-√3/2=√3(cos2x+1)/2+sin2x/2-√3/2=√3/2cos2x+√3/2+1/2sin2x-√3/2=1/2sin2x+√3/
f(x)=(sin²x+cos²x)+2cos²x+2√3sinxcosx-2=1+1+cos2x+√3sin2x-2=√3sin2x+cos2x=2sin(2x+π/6