函数f(x)=cos2x+2sinx,x∈(π/2,3π/4)的值域为

问题描述:

函数f(x)=cos2x+2sinx,x∈(π/2,3π/4)的值域为

f(x)=cos2x+2sinx=1-2sin²x+2sinx=-2(sin²x-sinx+1/4)+1/2+1=-2(sinx-1/2)²+3/2x∈(π/2,3π/4)-2(1-1/2)²+3/2<f(x)<-2(√2/2-1/2)²+3/21<f(x)<√2