求函数f(x)=[cos(x)+sin(x)]sin(x)的图像的对称点

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求函数f(x)=[cos(x)+sin(x)]sin(x)的图像的对称点
求函数f(x)=[cos(x)+sin(x)]sin(x)的图像的对称点

求函数f(x)=[cos(x)+sin(x)]sin(x)的图像的对称点
f(x)=[cos(x)+sin(x)]sin(x)=cos(x)sin(x)+sin^2(x)=1/2sin2x+1/2(1-cos2x)
=√2/2[cos(p/4)sin2x-sin(p/4)cos2x]+1/2=√2/2sin(2x-p/4)+1/2
2x-p/4=kp
x=(4k+1)p/8
图像的对称点:((4k+1)p/8,0) k为整数.