The sine function is negative in the third and fourth quadrants. Here’s the assessment of the given angles:
- \( \sin 120° \): This is in the second quadrant where sine is positive.
- \( \sin 0° \): This is on the x-axis where sine is zero, neither negative nor positive.
- \( \sin 270° \): This is in the fourth quadrant where sine is negative.
- \( \sin 90° \): This is at the top of the unit circle where sine is positive.
Therefore, the value at which \( \sin \theta \) is negative is \( \sin 270° \).