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Chapter 4: Problem 85

Find the absolute value of the radian measure of the angle that the second hand of a clock moves through in the given time. 3 minutes and 40 seconds

Short Answer

Expert verified
The second hand moves through an angle of \(11\pi/90\) radians.

Step by step solution

01

Conversion to seconds

First, convert the given time into seconds. The time given is '3 minutes and 40 seconds'. Since 1 minute equals to 60 seconds, the total time equals \(3 * 60 + 40=220\) seconds.
02

Calculation of radians

Next, calculate the amount of radians the second hand moves in 220 seconds. Use the fact established earlier, which is in 1 second, the second hand moves \(2\pi / 3600\) radians. Therefore, the second hand moves \(220 * (2\pi / 3600)\) radians.
03

Simplify

Simplify the expression to get the final result. Hence, the solution is \[220 * (2\pi / 3600) = 220 * (\pi /1800) = 11\pi/90\] radians.

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