An angle in standard position has its terminal side passing through the point $(0,-1)$ on the unit circle. Estimate the measure of this angle to the nearest one-half radian.

• A. $1.5$ radians
• B. $4.5$ radians
• C. $0.0$ radians
• D. $3.0$ radians

Answer: (B)

Verified step by step guidance

1. Identify the coordinates of the point on the unit circle, which are given as (0, -1). Since the point lies on the unit circle, its coordinates correspond to (cos(\theta), sin(\theta)) for some angle \theta in standard position.
2. Recognize that the x-coordinate is 0 and the y-coordinate is -1, so we have \cos(\theta) = 0 and \sin(\theta) = -1.
3. Recall the unit circle values where \sin(\theta) = -1 occurs. This happens at the angle where the terminal side points straight down along the negative y-axis.
4. Determine the angle \theta in radians that corresponds to this point. On the unit circle, the angle with \sin(\theta) = -1 and \cos(\theta) = 0 is \theta = \frac{3\pi}{2} radians.
5. Convert \frac{3\pi}{2} radians to a decimal approximation to estimate the angle measure to the nearest one-half radian.