Question

求定义域y=lg(3-4sin^2x)

-π/3 +kπ<x<kπ+π/3 ( k为整数.)
我画了一下图像，为什么不是-π/3 +3/4kπ<x<kπ+3/4π/3 ( k为整数.)

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Answer 1

求定义域y=lg(3-4sin^2x)
3-4sin^2x>0
sin^2x<3/4
则
-√3/2<sinx<√3/2
-π/3<x<π/3
2π/3<x<4π/3

各+2kπ
2kπ-π/3<x<2kπ+π/3
2kπ+2π/3<x<2kπ+4π/3

Answer 2

3-4sin²x>0

sin²x<3/4

-√3/2<sinx<√3/2
2kπ-π/3<x<2kπ+π/3,2kπ+2π/3<x<2kπ+4π/3
∴kπ-π/3<x<kπ+π/3

Answer 3

<-π/2+kπ,-π/3+kπ),(-π/6+kπ,π/6+kπ),(π/3+kπ,π/2+kπ>