Question

已知函数f(x)=2sin(k/3x+π/4),如果f(x)的周期在（2/3,3/4）内,求正整数k的值

Answer 1

已知函数f(x)=2sin(k/3x+π/4),如果f(x)的周期在（(2/3)π,(3/4)π）内,求正整数k的值.

ω=k/3.T=2π/ω=2π/(k/3)=6π/k

T≤(3/4)π --> 6π/k ≤ (3/4)π --> 8 ≤ k

T≥(2/3)π --> 6π/k ≥ (2/3)π --> k ≤ 9

结论：8 ≤ k ≤ 9 ,即,k = 8 或 9