求函数y=cos(x-π/3),x∈[-π/2,π/2]的值域,

题目

求函数y=cos(x-π/3),x∈[-π/2,π/2]的值域,

答案

设t=x-π/3,因为x∈[-π/2,π/2],所以t∈[-5π/6,π/6].因此求y=cos(x-π/3),x∈[-π/2,π/2]的值域就相当于求,t∈[-5π/6,π/6]的值域.当t=0时,y=cos0=1,此时为最大值；当t=-5π/6时,y=(-√3)/2；当t=π/6时,y=√3/...