函数f(x)=cos(2x+2π/3)+1的单调减区间怎么求
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函数f(x)=cos(2x+2π/3)+1的单调减区间怎么求
函数f(x)=cos(2x+2π/3)+1的单调减区间怎么求
函数f(x)=cos(2x+2π/3)+1的单调减区间怎么求
cosx的单调减区间:2kπ≤x≤2kπ+π
所以cos(2x+2π/3)+1的单调减区间:2kπ≤2x+2π/3≤2kπ+π
解得 2kπ-2π/3≤2x≤2kπ+π -2π/3
2kπ-2π/3≤2x≤2kπ+π/3
kπ-π/3≤x≤kπ+π/6
所以f(x)的单调减区间 [kπ-π/3,kπ+π/6]
化简为标准式子cosx2(x+π/3)+1,因为cosx的单间区间是“(0,π)+-2kπ,所以只需要将其缩减一半,在向左平移π/3,即原函数的单减区间是(-π/3,π/6)+-kπ