What is the angular position in radians of the minute hand of a clock at $5:00$, measured from the $12$ o'clock position in standard position (counterclockwise from the positive $x$-axis)?

• A. $\pi$
• B. $0$
• C. $\frac{5\pi }{6}$
• D. $\frac{\pi }{2}$

Answer: (B)

Verified step by step guidance

1. Understand that the minute hand of a clock completes a full circle (360 degrees or \$2\pi$ radians) every 60 minutes.
2. Calculate the angular displacement of the minute hand per minute by dividing the full circle by 60: \(\frac{2\pi}{60} = \frac{\pi}{30}\) radians per minute.
3. Determine the number of minutes past the hour at 5:00, which is 0 minutes, since the time is exactly on the hour.
4. Multiply the angular displacement per minute by the number of minutes past the hour to find the angular position: \$0 \times \frac{\pi}{30} = 0$ radians.
5. Interpret the result: the minute hand is at the 12 o'clock position, which corresponds to 0 radians measured counterclockwise from the positive x-axis (standard position).