1. The problem asks: In which quadrants is the sine function negative? 2. Recall that the sine function, $\sin(\theta)$, represents the y-coordinate of a point on the unit circle at an angle $\theta$ measured from the positive x-axis. 3. The unit circle is divided into four quadrants: - Quadrant I: angles from $0^\circ$ to $90^\circ$ (or $0$ to $\frac{\pi}{2}$ radians) - Quadrant II: angles from $90^\circ$ to $180^\circ$ (or $\frac{\pi}{2}$ to $\pi$ radians) - Quadrant III: angles from $180^\circ$ to $270^\circ$ (or $\pi$ to $\frac{3\pi}{2}$ radians) - Quadrant IV: angles from $270^\circ$ to $360^\circ$ (or $\frac{3\pi}{2}$ to $2\pi$ radians) 4. The sine function is positive when the y-coordinate is above the x-axis, which happens in Quadrants I and II. 5. The sine function is negative when the y-coordinate is below the x-axis, which happens in Quadrants III and IV. 6. Therefore, the sine function is negative in Quadrants III and IV. Final answer: The sine function is negative in Quadrants III and IV.