# What is the period of f(t)=sin( t /44 )+ cos( (7t)/24 ) ?

Aug 12, 2016

$528 \pi$

#### Explanation:

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

Here, the periods for the separate oscillations sin(t/44) and cos

(7t/24)$a r e$88pi and 48/7pi, respectively.

The period P for the compounded oscillation f(t) is given by

$P = L \left(88 \pi\right) = M \left(\frac{48}{7} \pi\right)$, where L and M are least positive integer

multiples to give P as the least even positive integer.

For .$L = 6 \mathmr{and} M = 77 , \le \ast P = 528 \pi$.

See how it works.

$f \left(t + P\right)$

$= f \left(t + 528 \pi\right)$

$= \sin \left(\frac{t}{44} + 24 \pi\right) + \cos \left(\frac{7}{24} t + 154 \pi\right)$

$= \sin \left(\frac{t}{44}\right) + \cos \left(\frac{7}{24} t\right)$

#=f(t).

Note the if P is halved , the second term would become its negative.