Question

The minute hand of a clock moves from 12 to 4 o'clock, or latex: \frac{1}{3} 1 3 of a complete rotation. through how many degrees does it move? through how many radians does it move?

Answer 1

The first thing you should keep in mind is that the watch can be modeled as a circle.

The full angle of a circle is equal to 360 degrees.

Therefore, for 1/3 of the circle we have:

 $(\frac{1}{3}) * (360) = 120$

Then, we have the following conversion:

π radians = 180 degrees

Applying the conversion we have:

 $(120) * (\frac{\pi }{180} ) = (\frac{2}{3} ) \pi$

Answer:

The movement of the clock hand in degrees and radians is:

Degrees = 120

Radians = $(\frac{2}{3} ) \pi$