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Chapter 5: Problem 88

The minute hand of a clock moves from 12 to 4 o'clock, or \(\frac{1}{3}\) of a complete revolution. Through how many degrees does it move? Through how many radians does it move?

Short Answer

Expert verified
The minute hand of a clock, by moving from 12 to 4 o'clock, turns through 120 degrees or \(\frac{2\pi}{3}\) radians.

Step by step solution

01

Calculate movement in degrees

Determine the part in degrees of the complete revolution moved by the minute hand. The minute hand of a clock completes a 360 degree turn in an hour. Given that the hand moved \(\frac{1}{3}\) of a revolution, find \(\frac{1}{3}\) of 360 degrees by multiplying \(\frac{1}{3} * 360 = 120\) degrees.
02

Calculate movement in radians

Find the part in radians moved by the minute hand. A complete revolution equates to \(2\pi\) radians. Therefore, \(\frac{1}{3}\) of a revolution is \((\frac{1}{3} * 2\pi) = \frac{2\pi}{3}\) radians.

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