2cos(x/2)-3sin(x/3)的周期怎么求
来源:百度知道 编辑:UC知道 时间:2024/06/21 01:13:33
2cos(x/2)-3sin(x/3)
令x=x+T
2cos((x+T)/2)-3sin((x+t)/3)
=2(cos(x/2)cos(T/2)-sin(x/2)sin(T/2))-3(sin(x/3)cos(T/3)+cos(x/3)sin(T/3))...............(1)
若T为周期,则原式和(1)式应该相等.
即:
cos(T/2)=1.....................(a)
sin(T/2)=0.....................(b)
cos(T/3)=1.....................(c)
sin(T/3)=0.....................(d)
由(a)(b):T/2=∏+k∏
=> T=2∏+2k∏ (k 为使得T为正数的整数,下同)
由(c)(d):T/3=∏+k'∏
=> T=3∏+3k'∏
因此当k=2,k'=1时T=6∏
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