Through how many radians does the minute hand turn from 4:12 to 4:47?
Answer and explanation
Correct answer: 7π/6
From 4:12 to 4:47, the elapsed time is 47 − 12 = 35 minutes. A minute hand completes one full revolution, equal to 2π radians, in 60 minutes. Therefore, its angular displacement in 35 minutes is (35/60) × 2π = 70π/60 = 7π/6 radians. Hence, option C is correct. The calculation uses the fraction of a complete revolution, not the clock reading itself. Option A corresponds to 25 minutes, option B to 30 minutes, and option D to 40 minutes of minute-hand motion. The direction would be clockwise, but the question asks only for the magnitude of the turn.
Frequently asked questions
What is the correct answer to this question?
7π/6
Why is this the correct answer?
From 4:12 to 4:47, the elapsed time is 47 − 12 = 35 minutes. A minute hand completes one full revolution, equal to 2π radians, in 60 minutes. Therefore, its angular displacement in 35 minutes is (35/60) × 2π = 70π/60 = 7π/6 radians. Hence, option C is correct. The calculation uses the fraction of a complete revolution, not the clock reading itself. Option A corresponds to 25 minutes, option B to 30 minutes, and option D to 40 minutes of minute-hand motion. The direction would be clockwise, but the question asks only for the magnitude of the turn.
Which subject and chapter does this question cover?
This is a Class 12 Mathematics question. Chapter: Trigonometric Functions. Topic: Angles.
