已知函数f(x)=(1+cos2x)sin平方x, - 知识问答

已知函数f(x)=(1+cos2x)sin平方x,x属于R,则f(x)的周期?奇偶?

3个回答

f(x)=(1+cos2x)(sinx)^2
=2(cosx)^2(sinx)^2
=(1/2)[sin(2x)]^2
=(1/2)[1-cos(4x)]/2
=(1/4)[1-cos(4x)]
=1/4-cos(4x)/4
最小正周期为π/2 ,周期为kπ/2.
f(-x)=1/4-cos(-4x)/4=1/4-cos(4x)/4=f(x)
函数是偶函数.

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