Question

What is the period of `f(t)=sin( t / 14 )+ cos( (t)/21 )`?

Answer 1

`84pi`

Explanation:

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

The periods of the two separate oscillations in f(t) are `28pi and 42pi`.

The period for the compounded oscillation is such that 28 M = 42 N, for lowest positive integers M and N. Easily, M =3 and N = 2. These give the LCM common value `84 pi` as the period for f(t).
`f(t+84pi)=sin(t/14+6pi)+cos(t/21+4pi)= sin(t/14)+cos(t/21)=f(t)`