1.4 Quostion 6, 1.4.43 HW Scores 33.33\%, 5 of 15 points Pointa: 0 of 1 Savo Identify the quadrant or quadrants for the angles satisfying the following conditions. \( \sin \alpha<0 \) and \( \cos \alpha<0 \) The angles \( \alpha \) satisfying the above conditions are in Quadrant (Type your answer as 1, 2, 3, or 4 . Use commas to separate answers if needed.)

To determine in which quadrant(s) the angle \( \alpha \) satisfies both \( \sin \alpha < 0 \) and \( \cos \alpha < 0 \), let's analyze each quadrant: 1. **Quadrant I**: - \( \sin \alpha > 0 \) - \( \cos \alpha > 0 \) - **Does not satisfy** the conditions. 2. **Quadrant II**: - \( \sin \alpha > 0 \) - \( \cos \alpha < 0 \) - **Only \( \cos \alpha \) is negative**. 3. **Quadrant III**: - \( \sin \alpha < 0 \) - \( \cos \alpha < 0 \) - **Both sine and cosine are negative**. 4. **Quadrant IV**: - \( \sin \alpha < 0 \) - \( \cos \alpha > 0 \) - **Only \( \sin \alpha \) is negative**. **Conclusion**: The angles \( \alpha \) that satisfy both \( \sin \alpha < 0 \) and \( \cos \alpha < 0 \) are in **Quadrant 3**. **Answer:** 3