sin2x-4分之 的最小值
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请采纳谢谢f(x)=(sin^4+cos^4+sin^2xcos^2x)/2-sin2x=((sin^2x+cos^2x)^2-sin^2xcos^2x)/2-sin2x=(1-sin^2xcos^2
f(x)=√[1^2+(√3)^2]·sin(2x+arctan√3/1)=2sin(2x+π/3),x∈[-π/4,π/4]∴易得f(x)min=f(-π/4)=-1
f'(x)=-2cos2x-acosx=-2(2(cosx)^2-1)-acosx=-4(cosx)^2-acosx+2=0cosx=(a+-sqrt(a^2+32))/-8sinx=sqrt(1-(
y=√3cos²x+1/2sin2x=√3/2(cos2x+1)+1/2sin2x=√3/2cos2x+1/2sin2x+√3/2=sin(π/3)cos2x+cos(π/3)sin2x+√
f(x)=[(sinx)^4+(cosx)^4+(sinx)^2(cosx)^2]/(2-sin2x)={[(sinx)^2+(cosx)^2]^2-(sinx)^2*(cosx)^2}/(2-2si
f(x)=(sin^4+cos^4+sin^2xcos^2x)/2-sin2x=((sin^2x+cos^2x)^2-sin^2xcos^2x)/2-sin2x=(1-sin^2xcos^2x)/2-
Y=(sin^4x+cos^4x+sin^2xcos^2x)/(2-sin2x)=((sin^2x+cos^2x)^2-sin^2xcos^2x)/(2-sin2x)=(1-sinxcosx)(1+s
y=sin2x+cos2x=根号2sin(2x+π/4)所以周期=2π/2=π;最大值=根号2最小值=-根号2取最大值时,2x+π/4=2kπ+π/22x=2kπ+π/4x=kπ+π/8取最小值时,2
y=根号2*(二分之根号2*sin2x+二分之根号2*cos2x)=根号2*(cos45°*sin2x+sin45°*cos2x)=根号2*sin(2x+45°)因为sin(2x+45°)在正负一之间
/>y=sin2x+2√2cos(π/4+x)+3=cos(2x-π/2)+2√2cos(π/4+x)+3=1-2sin²(x-π/4)-2√2sin(x-π/4)+3=4-2[sin
令π/4+x=Az则原式=sin(2A-π/2)+2√2cosA+3=-cos2A+2√2cosA+3=-2cosA^2+1+2√2cosA+3=-2(cosA-√2/2)^2+5由于cosA∈【-1
函数f(x)=根号3乘以sin2x+2cos^2x+m(x∈R)在区间02分之兀上的最小值为3,求f(x)的常数m的值解析:∵函数f(x)=√3sin2x+2cos^2x+m=√3sin2x+cos2
首先y=sin2x+2(cosx-sinx)+3,令cosx-sinx=t属于【-√2,√2】,所以y=-t^2+2t+4,由此易得其最小值为5.
令t=|sin2x|,则0≤t≤1,f(x)=根号下(1+|sin2x|)+|sin2x|^4=√(1+t)+t^4为关于t在[0,1]的增函数,故当t=0时,f(x)有最小值1,当t=1时,f(x)
f(x)=[(sin^2x+cos^2x)^2-sin^2xcos^2x]/(2-2sinxcosx)=(1-sinxcosx)(1+sinxcosx)/2(1-sinxcosx)=1/2sinxco
f(x)=sin2x+2(cosx)^2-1=sin2x+cos2x=√2[sin2xcos(π/4)+cos2xsin(π/4)]=√2sin(2x+π/4).∵π/4≦x≦3π/4,∴π/2≦2x
(|sinx|+|cosx|)^2=(sinx)^2+(cosx)^2+2|sinxcosx|=1+|sin(2x)|记t=|sin(2x)|f(x)=√(1+|sin(2x)|)+(sin2x)^4
cos(x+4分之派)=5分之3cosxcosπ/4-sinxsinπ/4=3/5√2/2(cosx-sinx)=3/5得:cosx-sinx=3√2/5(cosx-sinx)^2=cos^2x-2s
y=2cos²x-1+1+sin2x=sin2x+cos2x+1=√2(sin2x*√2/2+cos2x*√2/2)+1=√2(sin2xcosπ/4+cos2xsinπ/4)+1=√2si