正弦函数周期T=2π⼀丨ω丨怎么推导出来的

2025-04-07 09:51:30
推荐回答(3个)
回答1:

这个函数f(x)=sinx的周期是2π不用说吧
那f(x)=asinx的周期也就是2π
而f(x)=asin(x+φ)是f(x)=asinx将的图像向左平移φ个单位,周期不变,还是2π
现在我们把已知函数中的ωx作为整体,也是个自变量,看是不是就成了上面的函数了,它的周期表示式是2π<ωx<=2(n+1)π
然后不等式同时除以ω,就是2π/ω
+2π/ω
这个不等式的数学意义就是一直函数的周期是t=2π/ω

回答2:

(修正版)Y=sinX这个标准的正弦函数的周期才是2π..现在的函数是一个复合函数X=3x+3/4π..①x±c中c只是对函数起平移作用不影响周期..②ax中a是对函数进行关于原点,横向缩放的位似变换,a表示缩小为原来的1/a,也就是说:a>1表示缩小,0

回答3:

y=sin(ax+b),相当于y=sinx由x轴向左平移b,图像缩放a倍。由于原周期为2π,缩放后周期变为T=2π/a

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