Question

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

Answer 1

`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)`.