已知函数f(x)=根号3sin2x-2(sinx)^2 (1)若x属于【-30°,60°】,求f(X)的值域
问题描述:
已知函数f(x)=根号3sin2x-2(sinx)^2 (1)若x属于【-30°,60°】,求f(X)的值域
答
f(x)=sqrt(3)sin2x-2sinx^2=sqrt(3)sin2x+cos2x-1=2sin(2x+π/6)-1因为-π/6≤x≤π/3,所以-π/6≤2x+π/6≤5π/6当2x+π/6=-π/6,即x=-π/6时,f(x)取得最小值:2*(-1/2)-1=-2当2x+π/6=π/2,即x=π/6时,f(x)取得最...