On the unit circle, if point A is at $(1,0)$ and point D is at $(0,1)$, what is the measure in radians of the arc from A to D (arc AD)?

• A. $\frac{\pi }{4}$
• B. $\frac{\pi }{2}$
• C. $\pi$
• D. $2\pi$

Answer: (B)

Verified step by step guidance

1. Identify the coordinates of points A and D on the unit circle: A is at (1, 0) and D is at (0, 1).
2. Recall that on the unit circle, the angle in radians corresponding to a point (x, y) is the angle formed with the positive x-axis, measured counterclockwise.
3. Determine the angle for point A: since A is at (1, 0), it corresponds to an angle of 0 radians.
4. Determine the angle for point D: since D is at (0, 1), it corresponds to an angle of \( \frac{\pi}{2} \) radians (90 degrees).
5. Calculate the measure of the arc from A to D by finding the difference between their angles: \( \frac{\pi}{2} - 0 = \frac{\pi}{2} \) radians.