f(x)=根号3sin2x-2sin^2x
问题描述:
f(x)=根号3sin2x-2sin^2x
(1)若点P(1,-根号3)在角α的中边上,求f(α)的值
(2)若x∈【-π/6】,求f(x)的值域
第二题是若x∈【-π/6,π/3】,求f(x)的值域
答
(1)a=-60,sin(a)=-根号3/2,sin(2a)=-根号3/2带入得f(a)=-3(2)f(x)=根号3sin(2x)+cos(2x)-1=2sin(2x+π/6)-1x∈【-π/6,π/3】,则2x+π/6∈【-π/6,π5/6】,sin(2x+π/6)∈[-1/2,1]f(x)∈[-2,1]