https://file.aiquickdraw.com/mathbot/file/17264102300830bp2iyvx.jpg

The graph in the image shows a trigonometric function. Let's analyze it carefully:

- The function starts at 1 when \( x = 0 \), and then it decreases to -1 and back to 1, completing one full cycle by \( x = 360^\circ \).
- This behavior is characteristic of a cosine function.
- The period of the function is 360 degrees, which is typical for a cosine function with no horizontal stretch or compression.
- The amplitude (the height from the midline to the peak) is 1, and the graph goes from 1 to -1 and back to 1.

Based on these observations, the function displayed appears to be \( \cos(2x) \), which matches option **B**.

Would you like more details on how the cosine function works or further explanations?

Here are 5 related questions to think about:
1. What would the graph of \( \sin(2x) \) look like compared to \( \cos(2x) \)?
2. How does changing the coefficient of \( x \) in \( \cos(kx) \) affect the graph?
3. What happens if we change the amplitude of the function \( \cos(kx) \)?
4. How would the graph of \( \cos(x/2) \) compare to \( \cos(2x) \)?
5. What is the phase shift in trigonometric graphs, and how would it affect \( \cos(x) \)?

**Tip:** When identifying trigonometric graphs, pay attention to the starting point, the amplitude, and the period to match them to the correct function.

Which of the following trigonometric functions is displayed in the graph shown?

Learn how to identify trigonometric functions from their graphs. This problem focuses on recognizing the graph of the function cos(2x) by analyzing its period, amplitude, and shape. Suitable for high school students in Grades 10-12, this exercise covers key concepts in trigonometry and graphing.

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