What is the period of f(t)=sin( t / 36 )+ cos( (t)/64 ) ?

Jul 26, 2017

$1152 \pi$

Explanation:

Period $\sin \left(\frac{t}{36}\right)$ is $72 \pi$

Period $\cos \left(\frac{t}{64}\right)$ is $128 \pi$

Period of $\sin \left(\frac{t}{36}\right) + \cos \left(\frac{t}{64}\right)$ is the LCM times $\pi$

$L C M \left[64 , 128\right] = 1152$

So the period is $1152 \pi$