函数y=sin(3x+π/3)cos(x-π/6)+cos(3x+π/3)cos(x+π/3)的图象的一条对称轴的方
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![函数y=sin(3x+π/3)cos(x-π/6)+cos(3x+π/3)cos(x+π/3)的图象的一条对称轴的方](/uploads/image/z/62669-29-9.jpg?t=%E5%87%BD%E6%95%B0y%3Dsin%283x%2B%CF%80%2F3%29cos%28x-%CF%80%2F6%29%2Bcos%283x%2B%CF%80%2F3%29cos%28x%2B%CF%80%2F3%29%E7%9A%84%E5%9B%BE%E8%B1%A1%E7%9A%84%E4%B8%80%E6%9D%A1%E5%AF%B9%E7%A7%B0%E8%BD%B4%E7%9A%84%E6%96%B9)
函数y=sin(3x+π/3)cos(x-π/6)+cos(3x+π/3)cos(x+π/3)的图象的一条对称轴的方
函数y=sin(3x+π/3)cos(x-π/6)+cos(3x+π/3)cos(x+π/3)的图象的一条对称轴的方
函数y=sin(3x+π/3)cos(x-π/6)+cos(3x+π/3)cos(x+π/3)的图象的一条对称轴的方
cos(x+π/3)
=sin[π/2-(x+π/3)]
=sin(π/6-x)
=-sin(x-π/6)
所以y=sin(3x+π/3)cos(x-π/6)-cos(3x+π/3)sin(x-π/6)
=sin[(3x+π/3)-(x-π/6)]
=sin(2x+π/2)
=cos2x
cosx的对称轴用就是取最大或最小的地方,即x=kπ
所以此处是2x=kπ
x=kπ/2
cos(x+π/3)=-sin(x-π/6)
∴sin(3x+π/3)cos(x-π/6)+cos(3x+π/3)cos(x+π/3)
=sin(3x+π/3)cos(x-π/6)-cos(3x+π/3)sin(x-π/6)
=sin[(3x+π/3)-(x-π/6)]
=sin(2x+π/2)
=cos(2x)
∴对称轴为2x=kπ,即x=kπ/2,k∈Z
若取k=0,得x=0
y=sin(3x+π/3)cos(x-π/6)+cos(3x+π/3)cos(x+π/3)
=sin(3x+π/3)cos(x-π/6)+cos(3x+π/3)sin[π/2-(x+π/3)]
=sin(3x+π/3)cos(x-π/6)-cos(3x+π/3)sin(x-π/6)
=sin[(3x+π/3)-(x-π/6)]
=sin(2x+π/2)
=cos2x
其中一条对称轴的方程为x=π/2