Y=1/2sin2x+sin^2x
=1/2sin2x+(1-cos2x)/2
=1/2+√2/2(√2/2*sin2x-√2/2*cosx)
=1/2+√2/2sin(2x-π/4),
因为 sin(2x-π/4)∈[-1,1],
所以Y∈[1/2-√2/2,1/2+√2/2].