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What is the positive radian measure of the larger angle formed by the hands of a clock at 4 o'clock? Simplify your answ completely.

Ask by Delgado Malone. in the United States
Mar 11,2025

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The larger angle at 4 o'clock is \( \frac{4\pi}{3} \) radians.

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Bonus Knowledge

At 4 o'clock, the minute hand points at 12 (0 degrees), and the hour hand points at 4. Each hour mark on a clock represents 30 degrees since 360 degrees is divided by the 12 hours (360°/12 = 30°). Therefore, at 4 o'clock, the hour hand is at 4 * 30° = 120°. The angle between the hour hand and the minute hand is 120° - 0° = 120°. However, to find the larger angle, we subtract this from 360°: 360° - 120° = 240°. To convert 240 degrees to radians, we use the conversion factor π radians = 180 degrees: 240° * (π/180) = (240/180)π = (4/3)π radians. So, the positive radian measure of the larger angle formed by the hands of a clock at 4 o'clock is (4/3)π.

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