Question

Through how many radiars does the minute hand of a clock rotate from 12.40 PM to 1.30 PM? The thinste hand rotates theough radans. (Sumplity your answer. Type an exact answer in terms of π. Use integes or fractions for ary nambots in the expression)

Answer 1

From 12:40 PM to 1:30 PM, the minute hand of a clock rotates through ⅖π radians. This is calculated by considering the fraction of an hour that passes within those 50 minutes and multiplying it by 2π radians.

Step-by-step explanation:

To determine the angle in radians that the minute hand of a clock rotates from 12:40 PM to 1:30 PM, we need to consider the movement of the minute hand over this period of time. The minute hand completes one full rotation, or 2π radians, in 60 minutes. From 12:40 PM to 1:30 PM, the minute hand moves for 50 minutes, which is ⅓ of an hour.

We calculate the angle of rotation (Δθ) by multiplying the fraction of the hour by 2π radians:

Δθ = ⅓ hour × 2π radians

Δθ = ⅓ × 2π radians = ⅖π radians

So the minute hand rotates through ⅖π radians from 12:40 PM to 1:30 PM.