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The question asks to "Choose the correct graph" of the function \( y = \cos x \). Let's analyze the provided graphs:

The cosine function, \( y = \cos x \), has the following characteristics:
- Period: \( 2\pi \)
- Amplitude: 1 (meaning the graph oscillates between 1 and -1)
- Key points: At \( x = 0 \), \( \cos(0) = 1 \); at \( x = \frac{\pi}{2} \), \( \cos\left(\frac{\pi}{2}\right) = 0 \); at \( x = \pi \), \( \cos(\pi) = -1 \); and it continues this oscillating behavior between \( -1 \) and \( 1 \).

### Identifying the correct graph:
Looking at the options, option **C** matches the expected shape of the cosine function:
- The graph starts at \( y = 1 \) when \( x = 0 \).
- It crosses the x-axis at \( x = \frac{\pi}{2} \).
- It reaches a minimum value of \( y = -1 \) at \( x = \pi \).
- It follows the correct oscillation pattern within the range \( 0 \leq x \leq 2\pi \).

Therefore, **C** is the correct answer.

Would you like more details about the cosine function, or do you have any further questions?

Here are 5 related questions to deepen your understanding:
1. What is the amplitude and period of \( y = \sin x \) compared to \( y = \cos x \)?
2. How does the phase shift affect the graph of a cosine function?
3. What would the graph of \( y = \cos(2x) \) look like compared to \( y = \cos x \)?
4. How can the graph of \( y = \cos x \) be translated vertically?
5. What is the relationship between the graphs of \( y = \sin x \) and \( y = \cos x \)?

**Tip**: The graph of \( y = \cos x \) is periodic, meaning it repeats its shape every \( 2\pi \). Understanding this periodicity helps in recognizing transformations and translations of trigonometric functions.

Choose the correct graph of the function y = cos(x).

Learn how to identify the correct graph for the cosine function y = cos(x). This problem covers key trigonometric concepts such as amplitude, period, and the oscillating nature of cosine. Suitable for students in Grades 9-12.

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