What is the period of #f(t)=sin( t / 18 )+ cos( (t)/ 24 ) #?

1 Answer
Apr 26, 2016

#144pi#

Explanation:

The period for both sin kt and cos kt is #(2pi)/k#.

Here, the separate periods for the two terms are #36 pi and 48 pi#, respectively..

The compounded period for the sum is given by #L(36pi)=M(48pi)#, with the common vale as the least integer multiple of #pi#. The befitting L = 4 and M = 3 and the common LCM value is #144pi#.

The period of f(t) = #144pi#.

#f(t+144pi) = sin((t/18)+8pi)+cos((t/24)+6pi)=sin(t/18)+cos(t/24)=f(t)#.