=1+√3sin2x+1+cos2x
=2+√3sin2x+cos2x
=2+2sin(2x+π/6)
∴函数周期为2π/2=π.
已知函数f(x)=Sinx平方+根号3倍SinxCosx +2Cosx 平方,求f(x)的最小...
答：f(x)=(sinx)^2+√3sinxcosx+2(cosx)^2 =1+√3sinxcosx+(cosx)^2 =(√3\/2)sin2x+(1\/2)cos2x+1\/2+1 =sin(2x+π\/6)+3\/2 最小正周期T=2π\/2=π -π\/6<=x<=π\/3 -π\/3<=2x<=2π\/3 -π\/6<=2x+π\/6<=5π\/6 -1\/2<=sin(2x+π\/6)<=1 所以：-1\/2+...
...x)+3sin^2(3π\/2-x),求函数f(x)的最小证周期及单调递减区间。_百 ...
解： f(x)=(sinx)^2+2sinxcosx+3(cosx)^2=1+2(cosx)^2+sin2x=1+cos2x+1+sin2x=√2sin[2x+(π\/4)]+2 最小正周期:T=2π\/2=π 单调递减区间: 2x+(π\/4)∈[2kπ+π\/2,2kπ+3π\/2](k∈Z) x∈[kπ+π\/8,kπ+5π\/8](k∈Z)采纳哦 ...
已知函数f(x)=sin^2+2√3sinxcosx-cos^2x (1)求f(x)的最小正周期(2...
根据划一公式。原式=2Sin（2x-π\/6)根据公式ASin（Wx+N）。T=2π\/w 所以最小正周期为T=2π\/w=2π\/2=π 2.求最大值最小值。由1的2Sin（2x-π\/6)可知。正选函数。又已知F（x）区间为{0，π\/2} 由图像可知。所以。F（x）max=2 F(x)min=0 不懂HI我 ...
已知函数f(x)=sin²x+2根号3sinxcosx+3cos²x
f(x)=sinx^2+2√3sinxcosx+3cosx^2 =sinx^2+cosx^2+2√3sinxcosx+2cosx^2 =2√3sinxcosx+2cosx^2-1+2 =√3sin2x+cos2x+2 =2(√3\/2sin2x+1\/2cos2x)+2 =2sin(2x+π\/6)+2 剩下就简单了
已知f(x)=sinx^2+2sinxcosx+3cosx^2,x∈(0,π)
f(x)=sin²x+2sinxcosx+3cos²x ＝（1-cos2x）\/2+sin2x+3(1+cos2x)\/2 =√2sin(2x+π\/4)+2 (I) 函数f(x) 的最小正周期T=2π\/2=π ∵x∈(0,π)∴2x+π\/4∈(π\/4,9π\/4)当2x+π\/4=π\/2.即x=π\/x时，f(x)＝2+√2为最大值，当2x+π\/4=3π\/2....
已知函数f(x)=(sinx+cosx)^2+2倍根号3cos^2x,x属于R。1,求函数的最小...
f(x)=1+sin2x+根号3(1+cos2x)=sin2x+根号3cos2x+1+根号3=2sin(2x+π\/3)+1+√3 最小正周期T=2Pai\/2=Pai 单调减区间是2kPai+Pai\/2<=2x+Pai\/3<=2kPai+3Pai\/2 即有[kPai+Pai\/12,kPai+7Pai\/12]2.f(A)=2sin(2A+Pai\/3)+1+根号3=1+根号3 sin(2A+Pai\/3)=0 2A+Pai\/...
已知函数y =sin平方x+2sinxcosx+3cos平方x,求函数的最小正周期和函数...
y=(sinx)^2+2sinxcosx+3(cosx)^2=(1-cos2x)\/2+sin2x+3(1+cos2x)\/2=1\/2-(cos2x)\/2+sin2x+3\/2+3(cos2x)\/2=2+sin2x+cos2x=2+根号2sin(2x+∏\/4）最小正周期是2π\/2=π单调递增区间：由2Kπ-π\/2≤2x+∏\/4≤2kπ+π\/2，解得Kπ-3π\/8≤x≤kπ+π\/8，所以递增...
已知函数f(x)=sin^2+√3sinxcosx+2cos^2x,x属于R 坐等数学高手_百度...
f(x)=sin^2+√3sinxcosx+2cos^2x=f(x)=√3\/2sin2x+cos^2x+1=√3\/2sin2x+1\/2cos2x+3\/2=sin(2x+π\/6)+3\/2 1 最小正周期为π。对称轴方程为令sin(2x+π\/6)=±1，得x=π\/6+kπ，或者x=-π\/3+kπ 2、当sin(2x+π\/6)=1时，f(x0最大 x=π\/6+kπ 3、y=sinx...
已知函数f(x)=3sin²x+2√3sinxcosx+5cos²x 求函数f(x)的...
∴f(x)=4·sin^2 (x+π\/3) +2≤6;最大值是6.f(x)=4·sin^2 (x+π\/3) +2 =2·[2sin^2 (x+π\/3)-1] +2 +2 =-2·[1-2sin^2 (x+π\/3)]+4 =-2cos(2x+3π\/3)+4 则f（x）的最小正周期是2π\/2=π.f(a)=3sin^2 a+2√3sinacosa+5cos^2 a =5;∴3...
已知函数f(x)=sinxcosx+根号3\/2cos2x。(1)求f(x)的最小正周期T (2
已知函数f(x)=sinxcosx+根号3\/2cos2x。(1)求f(x)的最小正周期T(2)若三角形的三边a,b,c满足b^2=ac,且边b所对的角为B,求f(B)取值范围。急... 已知函数f(x)=sinxcosx+根号3\/2cos2x。(1)求f(x)的最小正周期T (2)若三角形的三边a,b,c满足b^2=ac,且边b所对的角为B,求f(B)取值范...
