f(x)=2cos*sin(x+π/3)-^3sin^2x+sinx*cosx1.求函数最小正周期2.求函数最大最小值3.求f(x)的递增区间
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![f(x)=2cos*sin(x+π/3)-^3sin^2x+sinx*cosx1.求函数最小正周期2.求函数最大最小值3.求f(x)的递增区间](/uploads/image/z/3248694-54-4.jpg?t=f%28x%29%3D2cos%2Asin%28x%2B%CF%80%2F3%29-%5E3sin%5E2x%2Bsinx%2Acosx1.%E6%B1%82%E5%87%BD%E6%95%B0%E6%9C%80%E5%B0%8F%E6%AD%A3%E5%91%A8%E6%9C%9F2.%E6%B1%82%E5%87%BD%E6%95%B0%E6%9C%80%E5%A4%A7%E6%9C%80%E5%B0%8F%E5%80%BC3.%E6%B1%82f%EF%BC%88x%EF%BC%89%E7%9A%84%E9%80%92%E5%A2%9E%E5%8C%BA%E9%97%B4)
f(x)=2cos*sin(x+π/3)-^3sin^2x+sinx*cosx1.求函数最小正周期2.求函数最大最小值3.求f(x)的递增区间
f(x)=2cos*sin(x+π/3)-^3sin^2x+sinx*cosx
1.求函数最小正周期
2.求函数最大最小值
3.求f(x)的递增区间
f(x)=2cos*sin(x+π/3)-^3sin^2x+sinx*cosx1.求函数最小正周期2.求函数最大最小值3.求f(x)的递增区间
f(x)=2cos*sin(x+π/3)-^3sin^2x+sinx*cosx
=2cosx(1/2sinx+√3/2cosx)-^3sin^2x+sinx*cosx
=sin2x+√3cos2x
=2sin(2x+π/3)
1.T=2π/2=π.
2.最大值2,最小值-2.
3.2kπ -π/2≤2x+π/3≤2kπ+π/2,
2kπ -5π/6≤2x+≤2kπ+π/6,
kπ -5π/12≤x≤kπ+π/12,
f(x)的递增区间是[kπ -5π/12,kπ+π/12]k∈Z.