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函数F(x)=sin2x%sinxCosx的最小值是( )A.0...

f'(x)=1/2cos2x*(2x)]+cosx =cos2x+cosx 显然这是偶函数 cos2x+cosx =2cos²x-1+cosx =2(cosx+1/4)²-9/8 -1

解: (1) f(x)=cos²x-√3sinxcosx+½ =½[1+cos(2x)]-(√3/2)sin(2x)+½ =½cos(2x)-(√3/2)sin(2x)+1 =cos(2x+π/3)+1 最小正周期T=2π/2=π cos(2x+π/3)=1时,f(x)取得最大值f(x)max=1+1=2 cos(2x+π/3)=-1时,f(x)取得最小值f(...

(1)f(x)=cos2x?sin2x+23sinxcosx+1=3sin2x+cos2x+1=2sin(2x+π6)+1.(4分)因此f(x)的最小正周期为π,最小值为-1.(6分)(2)由F(a)=2得2sin(2α+π6)+1=2,即2sin(2x+π6)=12,而由a∈[π4,π2],得2a+π6∈[23π,76π].(9分)故2a+π6=56...

∵f(x)=sin2x-2sinxcosx+3cos2x=1-2sinxcosx+2cos2x=1+1+cos2x-sin2x=-(sin2x-cos2x)+2=-2sin(2x-π4)+2.∴把函数f(x)的图象沿x轴向左平移m(m>0)个单位,得到函数g(x)的图象的解析式为:g(x)=-2sin(2x+2m-π4)+2.∵函数g(x)的图象关...

分子分母同除以 cos^2 x, 得 f(x) = 1/(tanx -tan^2 x) 0= 2√ 1/u(1-u) √ 1/u(1-u) >=2 1/u(1-u) >= 4 f(x) =cos^2x/(cosxsinx-sin^2x) = 1/(tanx -tan^2 x) = 1/u(1-u) >=4 最小值是4

f(x)=1+cosx+8sin2x2sinx=2cos2x2+8sin2x22sinx2cosx2=1+4tan2x2tanx2=4tanx2+1tanx2.∵x∈(0,π),∴x2∈(0,π2),∴tanx2>0,∴4tanx2+1tanx2≥4,当且仅当4tanx2=1tanx2,即tanx2=12时,函数f(x)=1+cosx+8sin2x2sinx的最小值为4.故答案为:4

f(x)=sin²x+2sinx f ′(x)=2sinxcosx+2cosx=2cosx(sinx+1) x∈(2kπ-π,2kπ+π)时,f ′(x)>0,f(x)单调增

(Ⅰ)∵f(x)=sinxcosx+sin2x,∴f(π4)=sinπ4cosπ4+sin2π4,…(1分)=(22)2+(22)2 …(4分)=1.…(6分)(Ⅱ)f(x)=sinxcosx+sin2x=12sin2x+1?cos2x2,…(8分)=12(sin2x?cos2x)+12=22sin(2x?π4)+12,…(9分)由x∈[0,π2]得 2x?π4∈[?π4,3π4],...

2x+π/3∈(π/3,4π/3) 2x+π/3看成一个整体a.取值a∈(π/3,4π/3) sin a (-√3/2,1]就是个sin的函数. 所以sin(2x+π/3)∈(-√3/2,1]

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