www.fltk.net > 已知函数F(x)=(sinx+根号3Cos)(Cosx%根号3sinx)

已知函数F(x)=(sinx+根号3Cos)(Cosx%根号3sinx)

1.f(x)=sinx/3cosx/3+根号3cos^2x/3=1/2 sin2x/3+根号3 /2 (cos2x/3+1)=sin(2x/3+pi/3)+根号3 /2对称中心的横坐标满足sin(2x/3+pi/3)=0,2x/3+pi/3=k pix=(3k-1)/2 pi2.cos x=(a^2+c^2-b^2)/(2ac)=(a^2+c^2-ac)/(2ac)>=(2ac-ac)/(2ac)=1/20

f(x)=(1/2)2sinx*cosx+√3*cosx^2=1/2sin2x+√3/2(2cos^2-1)+√3/2=1/2sin2x+√3/2cos2x+√3/2=cos60sin2x+cos2xsin60+√3/2=sin(2x+π/3))+√3/2T=2π/w=2π/2=π所以最小正周期是π

f(x)=sinx+根号3cosx=2*sin(x+pi/3) 1. T=2pi2. x用x-pi/3代替:y=sinx单调增区间:【0,pi/2】

f(x)=sinx/3cosx/3+√3cosx/3 -√3/2=1/2*2*SC+根号3/2*(2C方-1)=1/2*S2X/3+根号3/2*C2X/3=S(2X/3+PAI/3)最小正周期=2PAI*3/2=3PAI对称中心为所有的零点,2X/3+PAI/3=0,X=-PAI/2则对称中心为-PAI/2+K*3PAI/

f(x)=sinx/3cosx/3+根号3cos^2x/3 =1/2 sin2x/3+根号3 /2 (cos2x/3+1) =sin(2x/3+pi/3)+根号3 /2对称中心的横坐标满足sin(2x/3+pi/3)=0,2x/3+pi/3=k pix=(3k-1)/2 piT = 2π,对称中心为x=(3k-1)/2 pi祝您在新的一年一帆风顺,二龙腾飞,三羊开泰,四季平安,五福临门,六六大顺,七星高照,八方来财,九九同心,十全十美.

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) = sinx+√3 cosx= 2(sinxcosπ/3+cosxsinπ/3)= 2sin(x+π/3)周期=2π/1=2πx+π/3∈(2kπ+π/2,2kπ+3π/2)时递减∴递减区间为(2kπ+π/6,2kπ+7π/6),其中k∈Z

f(x)=√3cos^2x+sinxcosx-√3/2=√3/2*(cos2x+1)+1/2*sin2x-√3/2=√3/2cos2x+1/2sin2x=sin∏/3cos2x+sin2xcos∏/3=sin(2x+∏/3)下面的自己会做了吧?!自己细心算一下

f(x)=sinxcosx-√3(sinx)^2=1/2*sin(2x)-√3*[1-cos(2x)]/2=sin(2x+π/3)-√3/2 .1、平移后的表达式为 y=sin[2(x+a)]-b=sin(2x+2a)-b ,因此 2a=π/3 ,-b= -√3/2 ,解得 a=π/6 ,b=√3/2 .2、由 -π/2+2kπ<=2x+π/3<=π/2+2kπ ,得 -5π/12+kπ<=x<=π/12+kπ ,因此函数增区间是 [-5π/12+kπ,π/12+kπ] ,k∈Z .

(1)fx=sinx/3cosx/3+√3cosx/3 =1/2sin(2x/3)+√3/2[1+cos(2x/3)] =1/2sin(2x/3)+√32cos(2x/3)+√3/2 =sin(2x/3+π/3)+√3/2由2x/3+π/3=kπ+π/2得对称轴 x=kπ/2+π/12,k∈Z,由2x/3+π/3=kπ得对称中心横坐标 x=kπ/2-π/6,k∈Z,而纵坐标为√3/2∴对称中心为(kπ/2-π/6,√3/2),k∈Z.(2)∵0∴0sin5π/9】f(x)的值域为(√3,1+√3/2]

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