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

Feb 13, 2016

$T = \frac{2 \pi}{5} = {72}^{\circ}$

#### Explanation:

For any general cosine function of the form $f \left(t\right) = A \cos B t$, the amplitude is $A$ and represents the maximum displacement from the t-axis, and the period is $T = \frac{2 \pi}{B}$ and represents the number of units on the $t$ axis for a complete cycle or wavelength of the graph to pass by.

So in this particular case, the amplitude is $1$, and the period is $T = \frac{2 \pi}{5} = {72}^{\circ}$,

since by the conversion factor, ${360}^{\circ} = 2 \pi r a d$.

The graph is plotted below :

graph{cos(5x) [-2.735, 2.74, -1.368, 1.368]}