Question

find the positive radian measure of the angle that the second hand of a clock moves through in the given time. 4 minutes and 15 seconds. in 4 minutes and 15 seconds the second hand of a clock passes through an angle that measures radians. (simplify your answer. type your answer in terms of $pi$. use integers or fractions for any numbers in the expression.)

Explanation:

Step1: Convert time to seconds

1 minute = 60 seconds, so 4 minutes = 4×60 = 240 seconds. Total time is 240 + 15=255 seconds.

Step2: Know the angle per - second of second - hand

The second - hand of a clock makes a full rotation (2π radians) in 60 seconds. So the angle it moves per second is $\frac{2\pi}{60}=\frac{\pi}{30}$ radians per second.

Step3: Calculate the total angle

Multiply the angle per second by the total number of seconds. Angle = $\frac{\pi}{30}\times255=\frac{17\pi}{2}$ radians.

Answer:

$\frac{17\pi}{2}$