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The problem asks: 

**In the interval** \( \frac{5\pi}{3} < x < 2\pi \), **which of the trigonometric functions will be positive?**

This problem is about identifying the signs of the sine, cosine, and tangent functions in a specific interval of the unit circle.

### Step-by-Step Breakdown:

1. **Understanding the Interval**:
   - \( \frac{5\pi}{3} \) is equivalent to 300° in degrees.
   - \( 2\pi \) is equivalent to 360°.
   - So, the interval is from 300° to 360°, which is in the **fourth quadrant** of the unit circle.

2. **Trigonometric Function Signs in the Fourth Quadrant**:
   - In the fourth quadrant:
     - **Sine** is negative.
     - **Cosine** is positive.
     - **Tangent** is negative.

3. **Conclusion**:
   - The only positive function in the interval \( \frac{5\pi}{3} < x < 2\pi \) is **cosine**.

### Correct Answer:
- **B: cos(x)**

Let me know if you'd like more details or have any questions!

Here are some related questions:
1. What are the signs of trigonometric functions in each quadrant?
2. How do we convert radians to degrees in trigonometry?
3. What is the significance of the unit circle in trigonometry?
4. How do we calculate trigonometric values for angles larger than \( 2\pi \)?
5. What are the reference angles, and how do they affect trigonometric functions?

**Tip**: Always remember the mnemonic **"All Students Take Calculus"** to recall the signs of the trigonometric functions in each quadrant (All, Sine, Tangent, Cosine positive respectively).

In the interval 5π/3 < x < 2π, which of the trigonometric functions will be positive?

Explore which trigonometric functions are positive in the interval 5π/3 < x < 2π. This problem focuses on key trigonometric concepts, such as the unit circle and quadrant rules for sine, cosine, and tangent functions. Suitable for students in Grades 10-12.

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