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Chapter 4: Problem 86

Find the absolute value of the radian measure of the angle that the second hand of a clock moves through in the given time. 4 minutes and 25 seconds

Short Answer

Expert verified
The absolute value of the radian measure of the angle is \(28蟺\) radians.

Step by step solution

01

Convert minutes to seconds

Since everything here is based on the movement of the second hand, convert the given time into seconds for consistency. There are 60 seconds in a minute, so 4 minutes is equal to \(4*60=240\) seconds. So, the total time is 240 seconds + 25 seconds, which equals 265 seconds.
02

Calculate the degrees moved

The second hand of a clock moves at a rate of \(360掳/60s = 6掳\) per second. Therefore, over the course of 265 seconds, the second hand will move \(265*6=1590掳\).
03

Convert degrees to radians

Radians are another way of measuring angles. The formula to convert degrees to radians is \(掳*蟺/180\). Therefore, the movement of the second hand is \(1590掳*蟺/180 = 28蟺\) radians.

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