# What is the period of f(t)=sin( t / 32 )+ cos( (t)/36 ) ?

Oct 24, 2017

$576 \pi \approx 1809.557$

#### Explanation:

• The period of $\sin \left(\frac{t}{32}\right)$ is $32 \cdot 2 \pi = 64 \pi$

• The period of $\cos \left(\frac{t}{36}\right)$ is $36 \cdot 2 \pi = 72 \pi$

• The least common multiple of $64 \pi$ and $72 \pi$ is $576 \pi$, so that is the period of the sum.

graph{sin(x/32)+cos(x/36) [-2000, 2000, -2.5, 2.5]}