f(k)=sin(2t)+cos(3t)的周期

题目

f(k)=sin(2t)+cos(3t)的周期

答案

设最小正周期T,0＜T≤2π
根据定义:f(k+T)=f(k)
即：sin(2t+2T)+cos(3t+3T)=sin(2t)+cos(3t),
先用特殊值求出T,再验算.
令t=0,π,
sin2T+cos3T=1,sin2T-cos3T=-1,
∴sin2T=0,cos3T=1
T=2π