1. The problem asks how to determine the function values (sine or cosine) for given angles and how to identify if these values are positive, negative, or zero based on points on the unit circle. 2. The key formula is that for any angle $\theta$ on the unit circle: - $\sin \theta$ is the y-coordinate of the point on the circle. - $\cos \theta$ is the x-coordinate of the point on the circle. 3. Important rules: - The unit circle is centered at the origin with radius 1. - Angles are measured from the positive x-axis. - The sign of sine and cosine depends on the quadrant: - Quadrant I: $\sin \theta > 0$, $\cos \theta > 0$ - Quadrant II: $\sin \theta > 0$, $\cos \theta < 0$ - Quadrant III: $\sin \theta < 0$, $\cos \theta < 0$ - Quadrant IV: $\sin \theta < 0$, $\cos \theta > 0$ - On axes, sine or cosine can be 0. 4. To solve these questions: - Identify the angle $\theta$ and locate it on the unit circle. - Determine the coordinates of the point corresponding to $\theta$. - The sine value is the y-coordinate; cosine value is the x-coordinate. - Use the quadrant rules to decide if the value is positive, negative, or zero. 5. For example, $\sin 180^\circ = 0$ because the point is on the negative x-axis where y=0. 6. Practice by memorizing key angles and their sine and cosine values, and understanding the unit circle quadrants. This method helps you find function values and their signs quickly and accurately.