Question

What is the period of `f(t)=sin( t / 7 )+ cos( (t)/21 )`?

Answer 1

Period`=42pi`

Explanation:

`p_1=(2pi)/(1/7)=14pi`

`p_2=(2pi)/(1/21)=42pi`

the period for the sum is the `lcm(14pi, 42pi)=42pi`

Answer 2

nice Leland!...it's the same as a polyrhythm in music....LCMs are SO important!! If one musician is playing in one meter and a second musician is playing in another meter, you can manipulate all manner of LCMs for the sake of polyrhythms.

Here is a pretty TI screenshot to support the results.