函数y=3sin(kx+π/3)的最小周期T满足T∈(1,3),求正整数k并就最小的k值求出其单调区间及对称中心.尤其是对称中心那里
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![函数y=3sin(kx+π/3)的最小周期T满足T∈(1,3),求正整数k并就最小的k值求出其单调区间及对称中心.尤其是对称中心那里](/uploads/image/z/5243809-49-9.jpg?t=%E5%87%BD%E6%95%B0y%3D3sin%EF%BC%88kx%2B%CF%80%2F3%29%E7%9A%84%E6%9C%80%E5%B0%8F%E5%91%A8%E6%9C%9FT%E6%BB%A1%E8%B6%B3T%E2%88%88%EF%BC%881%2C3%EF%BC%89%2C%E6%B1%82%E6%AD%A3%E6%95%B4%E6%95%B0k%E5%B9%B6%E5%B0%B1%E6%9C%80%E5%B0%8F%E7%9A%84k%E5%80%BC%E6%B1%82%E5%87%BA%E5%85%B6%E5%8D%95%E8%B0%83%E5%8C%BA%E9%97%B4%E5%8F%8A%E5%AF%B9%E7%A7%B0%E4%B8%AD%E5%BF%83.%E5%B0%A4%E5%85%B6%E6%98%AF%E5%AF%B9%E7%A7%B0%E4%B8%AD%E5%BF%83%E9%82%A3%E9%87%8C)
函数y=3sin(kx+π/3)的最小周期T满足T∈(1,3),求正整数k并就最小的k值求出其单调区间及对称中心.尤其是对称中心那里
函数y=3sin(kx+π/3)的最小周期T满足T∈(1,3),求正整数k并就最小的k值求出其单调区间及对称中心.
尤其是对称中心那里
函数y=3sin(kx+π/3)的最小周期T满足T∈(1,3),求正整数k并就最小的k值求出其单调区间及对称中心.尤其是对称中心那里
2π/k=T∈(1,3),1
⑴ ∵T=2π/k (k为正整数),且T∈(1,3)
∴1 < 2π/k < 3
∴k=3,4,5,6.
⑵ k取最小值时,函数为y=3sin(3x+π/3) (下述中n为整数)
由2nπ –π/2 < 3x+π/3 < 2nπ + π/2
得2nπ/3 –5π/18 < x < 2nπ/3 + π/18
所以函数y=3sin(3x+π/...
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⑴ ∵T=2π/k (k为正整数),且T∈(1,3)
∴1 < 2π/k < 3
∴k=3,4,5,6.
⑵ k取最小值时,函数为y=3sin(3x+π/3) (下述中n为整数)
由2nπ –π/2 < 3x+π/3 < 2nπ + π/2
得2nπ/3 –5π/18 < x < 2nπ/3 + π/18
所以函数y=3sin(3x+π/3)的递增区间为[2nπ/3 –5π/18 ,2nπ/3 + π/18]
由2nπ + π/2 < 3x+π/3 < 2nπ + 3π/2
得2nπ/3 + π/18< x<2nπ/3 + 7π/18
所以函数y=3sin(3x+π/3)的递减区间为 [2nπ/3 + π/18 ,2nπ/3 + 7π/18]
由3x + π/3 = nπ 得x = nπ/3 - π/9
所以函数y=3sin(3x+π/3)的对称中心为(nπ/3 - π/9 ,0)
*说明:函数y=sinx 的最小周期是2π ,递增区间为[2nπ –π/2 , 2nπ + π/2],递减区间为[2nπ + π/2 , 2nπ + 3π/2],对称中心为(nπ ,0).(其中n为整数)
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