已知函数f(x)=4分之根号3sinx-4分之1cosx,若cosα=-13分之5,α∈[2...

解题如下：

解1：因为cosx=-5/13,x∈【π/2，π】，所以sinx=12/13 f(x)=√3/4（12/13）-1/4（-5/13）=（12√3+5）/52 2：把f(x)化简为：f(x)=1/2（√3/2sinx-1/2cosx）=1/2（cosπ/6sinx-sinπ/6cosx）=1/2sin（x-π/6）将函数f(x)的图像向右平移m个单位则变为：1/2si...

解：y=3sinx 4根号(1 cos2x)=3sinx 4根号[2(cosx)^2]在第一，第四象限 y=3sinx 4cosx*√2 在第二，第三象限 y=3sinx－4cosx*√2 无论都能化成y＝√41sin(x β)的形式 最大值√41

(1)若f(x)=1,求cos(2π/3-x)的值 f(x)=√3sin(x/4)cos(x/4)+cos^2(x/4)=√3/2sin(x/2)+1/2(2cos^(x/4)-1)+1/2 =sin(x/2)cos(π/6)+cos(x/2)sin(π/6)+1/2 =sin(x/2+π/6)+1/2 f(x)=1 sin(x/2+π/6)+1/2=1 sin(x/2+π/6)=1/2 x...

f(x)=1 sin(x/2+π/6)+1/2=1 sin(x/2+π/6)=1/2 x/2+π/6=π/6+2kπ x/2+π/6=5π/6+2kπ x/2=2kπ x/2=2π/3+2kπ x=4kπ x=4π/3+4kπ 2π/3-x=2π/3+4kπ 2π/3-x=-2π/3+4kπ cos(2π/3-x)=-√3/2 cos(2π/3-x)=-√3...

f(x)=根号3/2*sin2x-1/2cos2x=cospi/6sin2x-sinpi/6cos2x=sin(2x-pi/6)f(0)= -1/2 f(pi/4)=根号3/2 函数值的范围 [-1/2,根号3/2]

f(x)=4√3sinxcosx-4cos²x+1 =2√3sin(2x)-2[cos(2x)+1]+1 =2√3sin(2x)-2cos(2x) -1 =4[sin(2x)(√3/2)-cos(2x)(1/2)] -1 =4sin(2x -π/6) -1 x∈[0，π/2]0-π/6≤2x-π/6≤2·(π/2) -π/6 -π/6≤2x-π/6≤5π/6 -1/2≤sin(2x-...

因为sin(x-y)=sinxcosy-cosxsiny 所以 sin(a-4/π)=sinacos4/π-cosasin4/π=√2/2sina-√2/2cosa=5/13 sina-cosa=5√2/13 故cosa=sina-5√2/13 又因为 (sina)^2+(cosa)^2=1 把cosa=sina-5√2/13带入上式中可得 2(sina)^2-10√2/13(sina)-119/169=0 解得 sina=11...

[2分之1，1]

f(x)=√3sinx/4cosx/4+cos^2x/4=(√3/2)*sin(x/2)-(1/2)*cos(x/2)+1/2=sin(x/2-π/6)+1/2,当x=2π/3+4kπ或2π+4kπ时,f(x)=1,此时cos(2π/3-x)=1或-1/2.,6,