Question
in which quadrant would angle if sin angle = 1/2 and tan angle > 0? Use a digit for your response rather than a Roman numeral
Answers
GPT-4o mini
To determine the quadrant in which the angle lies, let's analyze the given conditions:
1. \( \sin \text{angle} = \frac{1}{2} \)
2. \( \tan \text{angle} > 0 \)
The sine function is positive in the first and second quadrants. Therefore, the angle could be in either quadrant.
Now, considering the tangent function: it is positive in the first and third quadrants. Since we need both sine to be \(\frac{1}{2}\) (which means the angle is either in the first or second quadrant) and tangent to be positive, the only quadrant that satisfies both conditions is the first quadrant.
Thus, the angle is in Quadrant 1.
The answer is **1**.
1. \( \sin \text{angle} = \frac{1}{2} \)
2. \( \tan \text{angle} > 0 \)
The sine function is positive in the first and second quadrants. Therefore, the angle could be in either quadrant.
Now, considering the tangent function: it is positive in the first and third quadrants. Since we need both sine to be \(\frac{1}{2}\) (which means the angle is either in the first or second quadrant) and tangent to be positive, the only quadrant that satisfies both conditions is the first quadrant.
Thus, the angle is in Quadrant 1.
The answer is **1**.