f(x)=4sin^2[(π+2x)/4].sinx+(cosx+sinx)(cosx-sinx)
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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
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
=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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