At which of the following values is sin θ negative?(1 point)

\( \sin(120^\circ) \): This angle is in the second quadrant, where sine is positive.
\( \sin(270^\circ) \): This angle is on the negative y-axis, where sine is negative.
\( \sin(0^\circ) \): This angle is at the origin (positive x-axis), where sine is zero.
\( \sin(90^\circ) \): This angle is on the positive y-axis, where sine is positive.

Question

At which of the following values is  sin θ  negative?(1 point)

sinθ=120°

sinθ=270°

sinθ=0°

sinθ=90°

GPT-4o mini · Accepted Answer

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) $**.