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The image you uploaded asks for the angle corresponding to \( \frac{5\pi}{4} \) radians, with multiple-choice options provided through different circular diagrams.

Let's break it down:

1. **Understanding the angle \( \frac{5\pi}{4} \):**
   - One full revolution around a circle in radians is \( 2\pi \) radians.
   - \( \frac{\pi}{4} \) is equivalent to 45°, so \( \frac{5\pi}{4} \) is \( 5 \times 45° = 225° \).

2. **Locating 225°:**
   - 225° is in the third quadrant of the unit circle.
   - It is measured counterclockwise from the positive x-axis, passing through 180°, and continuing 45° more into the third quadrant.

3. **Correct Choice:**
   - The diagram corresponding to \( \frac{5\pi}{4} \) should show an angle located in the third quadrant.
   - By observing the diagrams:
     - **Option C** represents an angle in the third quadrant, matching the position of 225°.

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

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Would you like a further breakdown or have any questions about radians and angles?

Here are 5 related questions to expand your understanding:

1. What is the relationship between degrees and radians?
2. How can you convert between radians and degrees?
3. How do you calculate angles in other quadrants using radians?
4. What are common angles in the unit circle, and their radian measures?
5. How does \( \frac{5\pi}{4} \) radians relate to reference angles?

**Tip:** To convert any angle from radians to degrees, multiply the radian measure by \( \frac{180}{\pi} \).

O ângulo a que se refere 5π/4 radianos é:

This problem helps students understand how to locate the angle of 5π/4 radians on the unit circle, which corresponds to 225°. It covers key trigonometric concepts like radians, degrees, and the unit circle, suitable for high school students.

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