y=2sinx+根号3cosx值域

题目

y=2sinx+根号3cosx值域

答案

y=2sinx+√3cosx
y/√7=(2/√7)sinx+(√3/√7)cosx
=cocarctan(√3/2)sinx+sinarctan(√3/2)cosx
=sin[x+arctan(√3/2)]
-1≤y/√7≤1
-√7≤y≤√7