To determine the period of the given function from the graph:

1. Definition of the period: The period of a function is the horizontal distance required for the function to complete one full cycle and repeat its pattern.

2. Analyze the graph:

   • Looking at the graph, observe that the function starts at $0$ on the $x$-axis, goes up, down, and completes one full cycle at $2\pi$.
   • This confirms that the function repeats every $2\pi$.

3. Answer: The period of the function is $2\pi$.

Correct option:

• $2\pi$

Would you like further clarification or details on how to find the period from different types of graphs?

Here are 5 follow-up questions to enhance your understanding:

1. How do you calculate the period of a sine or cosine function mathematically?
2. What is the relationship between the frequency and the period of a function?
3. How does the amplitude differ from the period in trigonometric functions?
4. If the period of a function is halved, how would the graph change?
5. Can non-sinusoidal periodic functions also have a defined period? Provide examples.

Tip: When determining the period from a graph, always measure the horizontal distance between two identical points in consecutive cycles!