Question
Identify the quadrant(s) of an angle \( \theta \) that satisfies the given conditions. \( \sin \theta>0, \cos \theta>0 \) Choose the correct answer below. A. I and IV B. I and II C. I D. I and III
Ask by Vargas Mitchell. in the United States
Feb 03,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
The angle \( \theta \) is in **Quadrant I**.
**Correct Answer:**
**C. I**
Solution
To determine the quadrant(s) where an angle \( \theta \) satisfies \( \sin \theta > 0 \) and \( \cos \theta > 0 \), let's analyze the signs of sine and cosine in each quadrant:
1. **Quadrant I:**
- \( \sin \theta > 0 \)
- \( \cos \theta > 0 \)
2. **Quadrant II:**
- \( \sin \theta > 0 \)
- \( \cos \theta < 0 \)
3. **Quadrant III:**
- \( \sin \theta < 0 \)
- \( \cos \theta < 0 \)
4. **Quadrant IV:**
- \( \sin \theta < 0 \)
- \( \cos \theta > 0 \)
Given the conditions \( \sin \theta > 0 \) and \( \cos \theta > 0 \), only **Quadrant I** satisfies both.
**Correct Answer:**
**C. I**
Reviewed and approved by the UpStudy tutoring team
Like
error msg
Explain 
Simplify this solution The Deep Dive
The angle \( \theta \) must be in the first quadrant to satisfy both conditions that \( \sin \theta > 0 \) and \( \cos \theta > 0 \). In the first quadrant (0 to 90 degrees), both sine and cosine values are positive. Hence, the correct answer is C. I. Now, if you’re ever in doubt about quadrants, remember this nifty tip: Just think of the unit circle! In the first quadrant, both x (cosine) and y (sine) coordinates are positive, making it the happy zone for angles!
