# What is the period of y= 3cos (2x)?

May 20, 2018

$\pi$

#### Explanation:

When looking at a generic trigonometric function

$y = A \cos \left(\omega x + \phi\right) + \beta$

the only factor involving the periodicity is $\omega$, i.e. the factor multiplying the variable. The formula for the period $T$ is

$T = \setminus \frac{2 \pi}{\omega}$

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

May 20, 2018

$\pi$

#### Explanation:

The equation is in the general form of $y = a \cos b x$
Where:
a = amplitude
b = used to find the period (T)

Since this graph is cosine, then the period (T) is $\frac{2 \pi}{n}$
The period is also the same for sine. However, it is different for tan. The period for tan is $\frac{\pi}{n}$

Why?
The period of a graph is basically asking you how long it takes for a graph to complete one oscillation ie how long does the graph take to return to its original position. So for sine and cosine, it takes $2 \pi$ seconds to complete one round but for tan, it takes $\pi$ seconds only

SO, the period for this graph is:
period(T) = $\frac{2 \pi}{n} = \frac{2 \pi}{2} = \pi$