# What is the period of f(t)=cos ( ( 7 t ) / 2 ) ?

May 16, 2016

$\frac{4 \pi}{7}$.

#### Explanation:

The period for both sin kt and cos kt is (2pi)/k.

Here, k = = $\frac{7}{2}$. So, the period is 4pi)/7..

See below how it works

$\cos \left(\left(\frac{7}{2}\right) \left(t + \frac{4 \pi}{7}\right)\right) = \cos \left(\frac{7 t}{2} + 2 \pi\right) = \cos \left(\frac{7 t}{2}\right)$

May 16, 2016

$T = \frac{4 \pi}{7}$

#### Explanation:

$y = A \cdot \cos \left(\omega \cdot t + \phi\right) \text{ general equation}$

$\text{A:Amplitude}$

$\omega : \text{Angular velocity}$

$\phi = \text{phase angle}$

$\text{your equation:} f \left(t\right) = \cos \left(\frac{7 t}{2}\right)$

$A = 1$

$\omega = \frac{7}{2}$

$\phi = 0$

$\omega = \frac{2 \pi}{T} \text{ T:Period}$

$\frac{7}{2} = \frac{2 \pi}{T}$

$T = \frac{4 \pi}{7}$