已知f(x)=sin(x+π/3)(1)当x∈R时,求f(x)的值域(2)当0≤x≤π/2时,求f(x)的值域
问题描述:
已知f(x)=sin(x+π/3)(1)当x∈R时,求f(x)的值域(2)当0≤x≤π/2时,求f(x)的值域
答
(1)y=sinx的值域是[-1,1]∴ y=sin(x+π/3)的值域是[-1,1](2)∵ 0≤x≤π/2∴ π/3≤x+π/3≤5π/6∴ x+π/3=π/2时,sin(x+π/3)有最大值1x+π/3=5π/6时,sin(x+π/3)有最大值1/2∴ y=sin(x+π/3)的值域是[1/2,1]...