Final answer:
Sine theta equals negative 1 when theta is StartFraction 3 pi Over 2 EndFraction (270 degrees), as this position on the unit circle has a y-coordinate of -1.
Step-by-step explanation:
The question asks for which value of theta sine theta equals negative 1. In the context of the unit circle, sine represents the y-coordinate of a point on the circle's circumference. Since the radius of the unit circle is 1, when sine theta equals -1, it means the point is at the lowest position on the circle, which corresponds to theta being StartFraction 3 pi Over 2 EndFraction or 270 degrees. This is because at this angle, the point lies on the negative y-axis, giving a sine value of -1.