# What is the period of f(t)=sin( t / 32 )+ cos( (t)/8 ) ?

Aug 11, 2016

$64 \pi$

#### Explanation:

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

Here, the separate periods for the oscillations

 sin(t/32) and cos (t/8) are

$64 \pi \mathmr{and} 16 \pi$, respectively.

The first is four times the second.

So, quite easily, the period for the compounded oscillation f(t) is

$64 \pi$

See how it works.

$f \left(t + 64 \pi\right)$

$= \sin \left(\frac{t}{32} + 3 \pi\right) + \cos \left(\frac{t}{8} + 8 \pi\right)$

$= \sin \left(\frac{t}{32}\right) + \cos \left(\frac{t}{8}\right)$

$= f \left(t\right)$.
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