2. All of the coordinates for special angles on the unit circle can be derived from the \( \qquad \) quadrant.

All of the coordinates for special angles on the unit circle can be derived from the **first** quadrant. **Explanation:** The unit circle is divided into four quadrants: 1. **First Quadrant (0° to 90°):** Both sine and cosine values are positive. 2. **Second Quadrant (90° to 180°):** Sine is positive, cosine is negative. 3. **Third Quadrant (180° to 270°):** Both sine and cosine values are negative. 4. **Fourth Quadrant (270° to 360°):** Sine is negative, cosine is positive. Special angles (like 30°, 45°, 60°, etc.) are typically first derived in the **first quadrant** where both sine and cosine are positive. Once these coordinates are known for the first quadrant, the signs can be adjusted appropriately for the other three quadrants based on the rules above. This simplifies the process of finding the coordinates for any special angle on the unit circle.