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

Period$= 42 \pi$

Explanation:

${p}_{1} = \frac{2 \pi}{\frac{1}{7}} = 14 \pi$

${p}_{2} = \frac{2 \pi}{\frac{1}{21}} = 42 \pi$

the period for the sum is the $\lcm \left(14 \pi , 42 \pi\right) = 42 \pi$

Jan 23, 2016

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.