Question

函数y=3sinx-根号3cosx在x属于［0,派］的值域

Answer 1

y=3sinx-√3cosx

=2√3(sinx*√3/2-cosx*1/2)

=2√3(sinx*cosπ/6-cosx*sinπ/6)

=2√3sin(x-π/6)

∵x∈［0,π］

∴x-π/6∈［-π/6,5π/6］

当x-π/6=-π/6时取得最小值2√3×（-1/2)=-√3

当x-π/6=π/2时取得最大值2√3×1=2√3

所以值域为[-√3,2√3]