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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?  

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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!

What is the period of the function graphed below?

Learn how to find the period of a trigonometric function from its graph. This step-by-step guide covers key concepts in graph analysis and periodic functions, using a clear example. Perfect for Grades 9-12 students studying trigonometry.

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