Problem 88 - Algebra and Trigonometry

Question

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?

Step-by-Step Solution

Answer

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 1: 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.

Step 2: 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.