求sin^4x+cos^4x+4sin^2xcos^2x-1的最小正周期及值域.

来源:学生作业帮助网 编辑:作业帮 时间:2024/12/01 18:28:54
求sin^4x+cos^4x+4sin^2xcos^2x-1的最小正周期及值域.
xN@ǟ_Sx3'/HRoBҘcRIL[ >;@gZN.L=nZT<#}rV% EĐA4huՀ.U]._-!`Zd6Yv;7JbvY+#)+E+kʊ7"p>̓ >.azjwZɄ8(M2O-Tȟp2RW mpl [ v/Mf[7 k=V{ո{yrEzEp5urpף~1s&{

求sin^4x+cos^4x+4sin^2xcos^2x-1的最小正周期及值域.
求sin^4x+cos^4x+4sin^2xcos^2x-1的最小正周期及值域.

求sin^4x+cos^4x+4sin^2xcos^2x-1的最小正周期及值域.
y=sin^4x+cos^4x+4sin^2xcos^2x-1
=(sin^2x+cos^2x)^2+2sin^2xcos^2x-1
=1+2sin^2xcos^2x-1
=2sin^2xcos^2x
=1/2*sin^2(2x)
=(1-cos4x)/4
=1/4-1/4*cos4x
周期T=2π/4=π/2
值域是:[0,1/2]
如果你认可我的回答,请点击左下角的“采纳为满意答案”,祝学习进步!
手机提问的朋友在客户端右上角评价点【满意】即可