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

Apr 26, 2016

$144 \pi$

Explanation:

The period for both sin kt and cos kt is $\frac{2 \pi}{k}$.

Here, the separate periods for the two terms are $36 \pi \mathmr{and} 48 \pi$, respectively..

The compounded period for the sum is given by $L \left(36 \pi\right) = M \left(48 \pi\right)$, with the common vale as the least integer multiple of $\pi$. The befitting L = 4 and M = 3 and the common LCM value is $144 \pi$.

The period of f(t) = $144 \pi$.

$f \left(t + 144 \pi\right) = \sin \left(\left(\frac{t}{18}\right) + 8 \pi\right) + \cos \left(\left(\frac{t}{24}\right) + 6 \pi\right) = \sin \left(\frac{t}{18}\right) + \cos \left(\frac{t}{24}\right) = f \left(t\right)$.