y=sinx(cosx+sinx).===>2y=2sinx(cosx+sinx)=2sinxcosx+2sin²x=sin2x+1-cos2x=(sin2x-cos2x)+1=(√2)sin[2x-(π/4)]+1.∴y=(√2/2)sin[2x-(π/4)]+(1/2).【1】易知,(1/2)-(√2/2)≤y≤(1/2)+(√2/2).即函数值域为[(1-√2)/2,(1+√2)/2].【2】易知,T=2π/2=π.即T=π
sinx(cosx+sinx)值域是 最小正周期是
y=sinx(cosx+sinx).===>2y=2sinx(cosx+sinx)=2sinxcosx+2sin²x=sin2x+1-cos2x=(sin2x-cos2x)+1=(√2)sin[2x-(π/4)]+1.∴y=(√2/2)sin[2x-(π/4)]+(1/2).【1】易知,(1/2)-(√2/2)≤y≤(1/2)+(√2/2).即函数值域为[(1-√2)/2,(1+√2)/2].【2】易知,T=2π/2=π.即T=π