求函数f(x)=2sin^2x +cos(x +π/3)单调增区间开头是sinx平方的二倍把步骤写清楚具体点 (把要点点出来)
来源:学生作业帮助网 编辑:作业帮 时间:2024/06/24 16:45:58
![求函数f(x)=2sin^2x +cos(x +π/3)单调增区间开头是sinx平方的二倍把步骤写清楚具体点 (把要点点出来)](/uploads/image/z/3810389-5-9.jpg?t=%E6%B1%82%E5%87%BD%E6%95%B0f%28x%29%3D2sin%5E2x+%2Bcos%28x+%2B%CF%80%2F3%EF%BC%89%E5%8D%95%E8%B0%83%E5%A2%9E%E5%8C%BA%E9%97%B4%E5%BC%80%E5%A4%B4%E6%98%AFsinx%E5%B9%B3%E6%96%B9%E7%9A%84%E4%BA%8C%E5%80%8D%E6%8A%8A%E6%AD%A5%E9%AA%A4%E5%86%99%E6%B8%85%E6%A5%9A%E5%85%B7%E4%BD%93%E7%82%B9+%EF%BC%88%E6%8A%8A%E8%A6%81%E7%82%B9%E7%82%B9%E5%87%BA%E6%9D%A5%EF%BC%89)
求函数f(x)=2sin^2x +cos(x +π/3)单调增区间开头是sinx平方的二倍把步骤写清楚具体点 (把要点点出来)
求函数f(x)=2sin^2x +cos(x +π/3)单调增区间
开头是sinx平方的二倍
把步骤写清楚具体点 (把要点点出来)
求函数f(x)=2sin^2x +cos(x +π/3)单调增区间开头是sinx平方的二倍把步骤写清楚具体点 (把要点点出来)
f(x)=cos(2x-π/3)+2sin(x-π/4)sin(x+π/4)
f(x)=1/2cos 2x+√3/2sin 2x+2(sin x-cos x)(xin x+cos x)
=1/2cos 2x+√3/2sin 2x-2(cos^2 x-sin^2 x)
=1/2cos 2x+√3/2sin 2x-2cos 2x
=-3/2cos 2x+√3/2sin 2x
=√3(1/2sin 2x-√3/2cos 2x)
=√3sin(2x-π/3)
1.可见,f(x)最小正周期为2π/2=π
图像为g(x)=√3sin(2x)向右平移π/6个单位得到
则对称轴为,x=kπ/2+5π/12(k∈Z)
2.令z=2x-π/3
由x∈[-π/12,π/2]
则z∈[-π/2,2π/3]
√3sin z∈[-√3,√3]
即f(x)值域为[-√3,√3]
f(x)=cos(2x-π/3)+2sin(x-π/4)sin(x+π/4)
f(x)=1/2cos 2x+√3/2sin 2x+2(sin x-cos x)(xin x+cos x)
=1/2cos 2x+√3/2sin 2x-2(cos^2 x-sin^2 x)
=1/2cos 2x+√3/2sin 2x-2cos 2x
=-3/2cos 2x+√3/2sin 2x
=√3(1/2sin 2x-√3/2cos 2x)
=√3sin(2x-π/3)