y=sinx+sin(2x)-cosx
=(sinx-cosx)+cos(π/2 -2x)
=√2sin(x-π/4)+cos[2(x-π/4)] 注意：cos(π/2-2x)=cos(2x-π/2).
=√2sin(x-π/4)+1-2sin²(x-π/4) 后面一項(xiàng)用二倍角公式.
=-2[sin(x-π/4)-(√2/4)]² +5/4 配方
sin(x-π/4)=√2/4時(shí),y有最大值ymax=5/4
sin(x-π/4)=-1時(shí),y有最小值ymin=-1-√2
綜上,得-1-√2≤y≤5/4,函數(shù)的值域?yàn)閇-1-√2,5/4].