f(x)=4sin^2[(π+2x)/4].sinx+(cosx+sinx)(cosx-sinx)①求最小周期②已知常数w>0,若函数y=f(wx)在区间[-π/2,2π/3]上是增函数,求w的取值范围③若方程f(x)(sinx-1)+a=0有解,求实数a的取值范围
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![f(x)=4sin^2[(π+2x)/4].sinx+(cosx+sinx)(cosx-sinx)①求最小周期②已知常数w>0,若函数y=f(wx)在区间[-π/2,2π/3]上是增函数,求w的取值范围③若方程f(x)(sinx-1)+a=0有解,求实数a的取值范围](/uploads/image/z/6908272-16-2.jpg?t=f%28x%29%3D4sin%5E2%5B%28%CF%80%2B2x%29%2F4%5D.sinx%2B%28cosx%2Bsinx%29%28cosx-sinx%29%E2%91%A0%E6%B1%82%E6%9C%80%E5%B0%8F%E5%91%A8%E6%9C%9F%E2%91%A1%E5%B7%B2%E7%9F%A5%E5%B8%B8%E6%95%B0w%3E0%2C%E8%8B%A5%E5%87%BD%E6%95%B0y%3Df%EF%BC%88wx%EF%BC%89%E5%9C%A8%E5%8C%BA%E9%97%B4%5B-%CF%80%2F2%2C2%CF%80%2F3%5D%E4%B8%8A%E6%98%AF%E5%A2%9E%E5%87%BD%E6%95%B0%2C%E6%B1%82w%E7%9A%84%E5%8F%96%E5%80%BC%E8%8C%83%E5%9B%B4%E2%91%A2%E8%8B%A5%E6%96%B9%E7%A8%8Bf%EF%BC%88x%EF%BC%89%EF%BC%88sinx-1%EF%BC%89%2Ba%3D0%E6%9C%89%E8%A7%A3%2C%E6%B1%82%E5%AE%9E%E6%95%B0a%E7%9A%84%E5%8F%96%E5%80%BC%E8%8C%83%E5%9B%B4)
f(x)=4sin^2[(π+2x)/4].sinx+(cosx+sinx)(cosx-sinx)①求最小周期②已知常数w>0,若函数y=f(wx)在区间[-π/2,2π/3]上是增函数,求w的取值范围③若方程f(x)(sinx-1)+a=0有解,求实数a的取值范围
f(x)=4sin^2[(π+2x)/4].sinx+(cosx+sinx)(cosx-sinx)
①求最小周期
②已知常数w>0,若函数y=f(wx)在区间[-π/2,2π/3]上是增函数,求w的取值范围
③若方程f(x)(sinx-1)+a=0有解,求实数a的取值范围
f(x)=4sin^2[(π+2x)/4].sinx+(cosx+sinx)(cosx-sinx)①求最小周期②已知常数w>0,若函数y=f(wx)在区间[-π/2,2π/3]上是增函数,求w的取值范围③若方程f(x)(sinx-1)+a=0有解,求实数a的取值范围
1,化简:f(x)=2(1-cos(π/2+x))sinx+(cosx)^2-(sinx)^2
=2sinx+1
T=2π
2,f(wx)=2sin(wx)+1
增区间[2kπ/w-π/2w,2kπ/w+π/2w] k是N.
[-π/2,2π/3]这个区间必须是上述区间的子集.
[2kπ/w-π/2w]=2π/3
解得:w
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