函数f(x)=sinx+根号3cosx,x属于[0,5/12x]求的取值范围

题目

函数f(x)=sinx+根号3cosx,x属于[0,5/12x]求的取值范围

答案

f(x)=sinx+根号3cosx
=2*(sinx*cosπ/3+cosx*sinπ/3)
=2sin(x+π/3)
因为0<=x<=5/12π,所以π/3<=x+π/3<=3/4π
sin(x+π/3)属于[2^(-1/2),1]
f(x)=2sin(x+π/3)属于[2^(1/2),2]
所以取值范围[2^(1/2),2]