已知y=2arcsin(cosx)的定义域为(-π/3,2π/3),求值域
问题描述:
已知y=2arcsin(cosx)的定义域为(-π/3,2π/3),求值域
答
x∈(-π/3,2π/3) ==> cosx∈(-1/2,1] ==> arcsin(cosx)∈(-π/6,π/2]
==> y∈(-π/3,π]
所以原函数的值域是:(-π/3,π].