What is the period of f(t)=sin(t2)+cos(13t24)?

1 Answer
Apr 25, 2016

52π

Explanation:

The period of both sin kt and cos kt is 2πk.

So, separately, the periods of the two terms in f(t) are 4πand(4813)π.

For the sum, the compounded period is given by L(4π)=M((4813)π), making the common value as the least integer multiple of π.

L=13 and M=1. The common value = 52π;

Check: f(t+52π)=sin((12)(t+52π))+cos((2413)(t+52π))
=sin(26π+t2)+cos(96π+(2413)t)
=sin(t2)+cos(2413t)=f(t)..