The period of the function in the graph is P = 12pi
How to determine the period of a graph?
A function f(x) has a period P if for any value of x is true that:
f(x) =f(x + n*P)
Where n is any integer.
To find the period in this graph, just look at the distance between two consecutive maxima.
The first maxima is at:
x = 3pi
The next maxima is at:
x = 15pi
The period is the difference between these two values.
P = 15pi - 3pi = 12pi