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

Aug 14, 2016

$36 \pi$

#### Explanation:

For both sin kt and cos kt, the period is $2 \frac{\pi}{k}$.

Here, the periods for the separate oscillations

$\sin \left(\frac{t}{18}\right) \mathmr{and} \cos \left(\frac{t}{18}\right)$ are the same $36 \pi$.

And so, for the compounded oscillation

$f \left(t\right) = \sin \frac{t}{18} + \cos \frac{t}{18}$ also the period (= even LCM of separate

periods) is the common value $36 \pi$