Question

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

Answer 1

`pi`

Explanation:

When looking at a generic trigonometric function

`y = Acos(omega x + phi) + beta`

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

`T = \frac{2pi}{omega}`

So. in your case,

`T = \frac{2pi}{2} = pi`

Answer 2

`pi`

Explanation:

The equation is in the general form of `y=acosbx`
Where:
a = amplitude
b = used to find the period (T)

Since this graph is cosine, then the period (T) is `(2pi)/n`
The period is also the same for sine. However, it is different for tan. The period for tan is `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 `2pi` seconds to complete one round but for tan, it takes `pi` seconds only

SO, the period for this graph is:
period(T) = `(2pi)/n = (2pi)/2 = pi`