Problem 87 - Algebra and Trigonometry

Question

The minute hand of a clock moves from 12 to 2 o'clock, or \(\frac{1}{6}\) 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 moves 60 degrees and \(\frac{\pi}{3}\) radians from 12 to 2 o'clock.

Step 1: Understanding Full Revolution

A full revolution or cycle is 360 degrees or \(2\pi\) radians. This is a fundamental concept in understanding degrees and radians.

Step 2: Calculate Degrees

To find the degrees that the minute hand moves from 12 to 2, multiply 360 degrees by \(\frac{1}{6}\) because the minute hand has moved \(\frac{1}{6}\) of a full revolution. \(360 \times \(\frac{1}{6} = 60\). So, the minute hand moves 60 degrees.

Step 3: Calculate Radians

To find the radian measure for the same movement, multiply \(2\pi\) radians (complete revolution) by \(\frac{1}{6}\) to get \(2\pi \times \frac{1}{6} = \frac{\pi}{3}\) radians. So, the hand moves \( \frac{\pi}{3} \) radians.