函数y=sin²x﹢2cosx的值域为

y=sin²x﹢2cosx
= 1-(cosx)^2 +2cosx
= -(cosx-1)^2+2
值域[1,2]x∈[-π／3,2π／3]值域为y=2-(cosx-1)^2x∈[-π／3,2π／3]max y = y(0) = 2min y = y(2π/3) = 2- ( -1/2-1)^2 = 2- 9/4 = -1/4 值域[-1/4,2]