已知函数f(x)=sin^4x+cos^4x(1)求的值域,最小正周期和单调区间；（2）绘出f(x)在{-π/2,π/2}上的草图.如题

Question

已知函数f(x)=sin^4x+cos^4x (1)求的值域,最小正周期和单调区间；（2）绘出f(x)在{-π/2,π/2}上的草图.
如题

Answer 1

=(sin^2x+cos^2x)^2-2sin^2xcos^2x
=1-2sin^2xcos^2x
=1-0.5*(2sin2xcos2x)^2
=1-0.5sin^2(2x)
=1-0.5*0.5(1-cos4x)
=0.75+0.25cos4x
然后自己算吧