Question
At which of the following values is sin θ negative?(1 point)
sinθ=120°
sinθ=270°
sinθ=0°
sinθ=90°
sinθ=120°
sinθ=270°
sinθ=0°
sinθ=90°
Answers
GPT-4o mini
The sine function, \( \sin \theta \), is negative in the third and fourth quadrants of the unit circle.
Let's analyze the given angles:
1. **\( \sin(120^\circ) \)**: This angle is in the second quadrant, where sine is positive.
2. **\( \sin(270^\circ) \)**: This angle is on the negative y-axis, where sine is negative.
3. **\( \sin(0^\circ) \)**: This angle is at the origin (positive x-axis), where sine is zero.
4. **\( \sin(90^\circ) \)**: This angle is on the positive y-axis, where sine is positive.
Based on this analysis, the only angle where \( \sin \theta \) is negative is:
**\( \sin(270^\circ) \)**.
Let's analyze the given angles:
1. **\( \sin(120^\circ) \)**: This angle is in the second quadrant, where sine is positive.
2. **\( \sin(270^\circ) \)**: This angle is on the negative y-axis, where sine is negative.
3. **\( \sin(0^\circ) \)**: This angle is at the origin (positive x-axis), where sine is zero.
4. **\( \sin(90^\circ) \)**: This angle is on the positive y-axis, where sine is positive.
Based on this analysis, the only angle where \( \sin \theta \) is negative is:
**\( \sin(270^\circ) \)**.