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

The coordinates for special angles on the unit circle can primarily be derived from the first quadrant, where both the sine and cosine values are positive. In this quadrant, the common special angles are 0°, 30°, 45°, 60°, and 90°, which correspond to the coordinates (1, 0), \((\frac{\sqrt{3}}{2}, \frac{1}{2})\), \((\frac{\sqrt{2}}{2}, \frac{\sqrt{2}}{2})\), \((\frac{1}{2}, \frac{\sqrt{3}}{2})\), and (0, 1) respectively. From these coordinates, you can easily find values in the other three quadrants by applying the properties of sine and cosine, allowing you to cover all angles in the unit circle, just like a spectacular fireworks display that continues to dazzle in the night sky!