y=3sin(2x+π/6)单调减区间

1个回答

  • 令z=2x+π/6 则y=3sinz

    sinz 函数在 [ -π/2+2kπ,π/2+2kπ ]区间单调递增;

    [ π/2+2kπ,3π/2+2kπ ]区间单调递减 k=0,±1,±2,±3……

    当 -π/2+2kπ ≤ z ≤ π/2+2kπ 单调递增

    -π/2+2kπ ≤ 2x+π/6 ≤ π/2+2kπ

    所以 -π/3+kπ ≤ x ≤ π/6+kπ

    [-π/3+kπ ,π/6+kπ] 单调递增

    当 π/2+2kπ≤ z ≤ 3π/2+2kπ 单调递减

    π/2+2kπ≤ 2x+π/6 ≤ 3π/2+2kπ

    所以 π/6+kπ ≤ x ≤ 2π/3+kπ

    [ π/6+kπ,2π/3+kπ] 单调递减