已知y=sin²x+2根号3sinxcosx+3cos²x 求函数最小正周期和单调递增区间
来源:学生作业帮助网 编辑:作业帮 时间:2024/07/06 17:00:42
![已知y=sin²x+2根号3sinxcosx+3cos²x 求函数最小正周期和单调递增区间](/uploads/image/z/3709614-30-4.jpg?t=%E5%B7%B2%E7%9F%A5y%3Dsin%26%23178%3Bx%2B2%E6%A0%B9%E5%8F%B73sinxcosx%2B3cos%26%23178%3Bx+%E6%B1%82%E5%87%BD%E6%95%B0%E6%9C%80%E5%B0%8F%E6%AD%A3%E5%91%A8%E6%9C%9F%E5%92%8C%E5%8D%95%E8%B0%83%E9%80%92%E5%A2%9E%E5%8C%BA%E9%97%B4)
已知y=sin²x+2根号3sinxcosx+3cos²x 求函数最小正周期和单调递增区间
已知y=sin²x+2根号3sinxcosx+3cos²x 求函数最小正周期和单调递增区间
已知y=sin²x+2根号3sinxcosx+3cos²x 求函数最小正周期和单调递增区间
y=1-(cosx)^2+3(cosx)^2+√3sin2x
=1+2(cosx)^2+√3sin2x
=cos2x+√3sin2x+2
=2(sinπ/6cos2x+cosπ/6sin2x)+2
=2sin(2x+π/6)+2
最小正周期T=2π/2=π,
2kπ-π/2≤2x+π/6≤2kπ+π/2,为单调增函数,
kπ-π/3≤x≤kπ+π/6,k∈Z,
2kπ+π/2≤2x+π/6≤2kπ+3π/2,为单调减函数,
kπ+π/6≤x≤kπ+2π/3,k∈Z.