Question

函数f(x)=-根号3sinx+cosx(x属于-pi/2,pi/2)的值域为

Answer 1

f(x)=-√3sinx+cosx=-2[sinxcosπ/6-cosxsinπ/6]=-2sin(x-π/6)

∵-π/2≤x≤π/2

∴-2π/3≤x-π/6≤π/3

∴-1≤sin(x-π/6)≤√3/2

即-√3≤f(x)≤2

即值域为[-√3,2]