locate and mark point in the unit circle for 3PI/2

On the unit circle, angles are measured in radians, starting from \(0\) radians (or \(0^\circ\)) at the positive \(x\)-axis and increasing counterclockwise.

### To locate \( \frac{3\pi}{2} \):

1. **Convert to degrees** (if needed):  
   \[ \frac{3\pi}{2} \text{ radians} = 270^\circ \]

2. **Position on the unit circle**:  
   An angle of \(270^\circ\) corresponds to the point on the negative \(y\)-axis.

3. **Coordinates**:  
   The coordinates of this point are \((0, -1)\), because the point is directly down from the origin on the unit circle.

So, the point corresponding to \( \frac{3\pi}{2} \) on the unit circle is **(0, -1)**.

Would you like more details on how the unit circle works, or do you have any questions?

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Here are some related questions:
1. What are the coordinates for \( \frac{\pi}{2} \) on the unit circle?
2. Can you explain why \( \frac{3\pi}{2} \) corresponds to \(270^\circ\)?
3. How do you convert between degrees and radians?
4. What is the importance of the unit circle in trigonometry?
5. How would you locate \( \frac{7\pi}{4} \) on the unit circle?

**Tip**: Always remember that a full circle is \(2\pi\) radians or \(360^\circ\). This helps in converting and understanding angle positions easily.

Understand how to locate and mark the point for 3π/2 on the unit circle. This problem involves converting radians to degrees and identifying the coordinates corresponding to 270 degrees on the unit circle. Perfect for students in Grades 10-12.

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