What is the period of f(t)=cos ( ( 5 t ) / 2 ) ?

May 3, 2016

$T = \frac{1}{f} = \frac{2 \pi}{\omega} = \frac{4 \pi}{5}$

Explanation:

One way to get the period from a sinusoid is to recall that the argument inside the function is simply the angular frequency, $\omega$, multiplied by the time, $t$

$f \left(t\right) = \cos \left(\omega t\right)$

which means that for our case

$\omega = \frac{5}{2}$

The angular frequency is related to the normal frequency by the following relation:

$\omega = 2 \pi f$

which we can solve for $f$ and plug in our value for the angular frequency

$f = \frac{\omega}{2 \pi} = \frac{5}{4 \pi}$

The period, $T$, is just the reciprocal of the frequency:

$T = \frac{1}{f} = \frac{4 \pi}{5}$