Question
Question
In which quadrant would θ be if sinθ=12 and tanθ>0 ? Use a digit for your response rather than a Roman numeral.(1 point)
Quadrant
Answers
GPT-4o mini
To determine the quadrant in which the angle \( \theta \) is located, we analyze the given values of \( \sin \theta \) and \( \tan \theta \).
1. **Given**: \( \sin \theta = \frac{1}{2} \)
The sine function is positive in Quadrants I and II.
2. **Given**: \( \tan \theta > 0 \)
The tangent function is positive in Quadrants I and III.
Now we combine this information:
- Since \( \sin \theta \) is positive, \( \theta \) can be in Quadrant I or II.
- Since \( \tan \theta \) is positive, \( \theta \) can only be in Quadrant I (where both sine and cosine are positive) because it cannot be in Quadrant II (where sine is positive, but cosine is negative).
Therefore, the angle \( \theta \) is in **Quadrant 1**.
The answer is: **1**
1. **Given**: \( \sin \theta = \frac{1}{2} \)
The sine function is positive in Quadrants I and II.
2. **Given**: \( \tan \theta > 0 \)
The tangent function is positive in Quadrants I and III.
Now we combine this information:
- Since \( \sin \theta \) is positive, \( \theta \) can be in Quadrant I or II.
- Since \( \tan \theta \) is positive, \( \theta \) can only be in Quadrant I (where both sine and cosine are positive) because it cannot be in Quadrant II (where sine is positive, but cosine is negative).
Therefore, the angle \( \theta \) is in **Quadrant 1**.
The answer is: **1**