已知函数f(x)=根号3(sinx^2-cosx^2)-2sinxcosx⑴ 求f(x)的最小正周期...已知函数f(x)=根号3(sinx^2-cosx^2)-2sinxcosx⑴ 求f(x)的最小正周期 ⑵设x∈[-π/3,π/3],求f(x)的值域和单调
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![已知函数f(x)=根号3(sinx^2-cosx^2)-2sinxcosx⑴ 求f(x)的最小正周期...已知函数f(x)=根号3(sinx^2-cosx^2)-2sinxcosx⑴ 求f(x)的最小正周期 ⑵设x∈[-π/3,π/3],求f(x)的值域和单调](/uploads/image/z/1700365-13-5.jpg?t=%E5%B7%B2%E7%9F%A5%E5%87%BD%E6%95%B0f%EF%BC%88x%EF%BC%89%EF%BC%9D%E6%A0%B9%E5%8F%B73%EF%BC%88sinx%5E2%EF%BC%8Dcosx%5E2%EF%BC%89%EF%BC%8D2sinxcosx%E2%91%B4+%E6%B1%82f%EF%BC%88x%EF%BC%89%E7%9A%84%E6%9C%80%E5%B0%8F%E6%AD%A3%E5%91%A8%E6%9C%9F...%E5%B7%B2%E7%9F%A5%E5%87%BD%E6%95%B0f%EF%BC%88x%EF%BC%89%EF%BC%9D%E6%A0%B9%E5%8F%B73%EF%BC%88sinx%5E2%EF%BC%8Dcosx%5E2%EF%BC%89%EF%BC%8D2sinxcosx%E2%91%B4+%E6%B1%82f%EF%BC%88x%EF%BC%89%E7%9A%84%E6%9C%80%E5%B0%8F%E6%AD%A3%E5%91%A8%E6%9C%9F+%E2%91%B5%E8%AE%BEx%E2%88%88%5B%EF%BC%8D%CF%80%2F3%2C%CF%80%2F3%5D%2C%E6%B1%82f%EF%BC%88x%EF%BC%89%E7%9A%84%E5%80%BC%E5%9F%9F%E5%92%8C%E5%8D%95%E8%B0%83)
已知函数f(x)=根号3(sinx^2-cosx^2)-2sinxcosx⑴ 求f(x)的最小正周期...已知函数f(x)=根号3(sinx^2-cosx^2)-2sinxcosx⑴ 求f(x)的最小正周期 ⑵设x∈[-π/3,π/3],求f(x)的值域和单调
已知函数f(x)=根号3(sinx^2-cosx^2)-2sinxcosx⑴ 求f(x)的最小正周期...
已知函数f(x)=根号3(sinx^2-cosx^2)-2sinxcosx⑴ 求f(x)的最小正周期 ⑵设x∈[-π/3,π/3],求f(x)的值域和单调递增区间
已知函数f(x)=根号3(sinx^2-cosx^2)-2sinxcosx⑴ 求f(x)的最小正周期...已知函数f(x)=根号3(sinx^2-cosx^2)-2sinxcosx⑴ 求f(x)的最小正周期 ⑵设x∈[-π/3,π/3],求f(x)的值域和单调
f(x)=根号3(sinx^2-cosx^2)-2sinxcosx
=-√3cos2x-sin2x
=-2sin(2x+π/3)
最小正周期为 2π/2=π
x∈[-π/3,π/3],
则 2x+π/3∈[-π/3,π]
所以值域为 [-2,√3]
单调增区间:
2x+π∈[π/2,π]
x∈[-π/4,0]
所以
单调增区间为 [-π/4,0]
f(x)=-√3cos2x-sin2x
=-2(sin2x*cosπ/3+cos2xsinπ/3)
=-2sin(2x+π/3)
所以T=2π/2=π
-π/3<=x<=π/3
-π/3<=2x+π/3<=π/2
此范围sin递增,则-2sin(2x+π/3)递减
所以-2sin(-π/3)=√3,-2sin(π/2)=-2
值域[-2,√3]
减区间是[-π/3,π/3]