Question

Find the positive radian measure of the angle that the second hand of a clock goes through at 40 seconds.

a) 2π/3
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b) 4π/3
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c) 5π/3
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d) 7π/3
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Answer 1

The positive radian measure of the angle for the second hand of a clock at 40 seconds is 4π/3 radians, which is option b).

Step-by-step explanation:

The second hand of a clock completes one full rotation, which is 2π radians, in 60 seconds. To find the angle that the second hand goes through at 40 seconds, you would calculate the fraction of the full rotation based on the time:

Angle of rotation = (Time in seconds / 60 seconds) × 2π radians = (40 / 60) × 2π radians

Angle of rotation = (2/3) × 2π radians = 4π/3 radians

Therefore, the positive radian measure of the angle is 4π/3, which corresponds to option b).