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Question

Mathematics Question on Trigonometric Functions

The large hand of a clock is 42cm42 \,cm long. How much distance does its extremity move in 2020 minutes?

A

88cm88 \,cm

B

80cm80 \,cm

C

75cm75 \,cm

D

77cm77 \,cm

Answer

88cm88 \,cm

Explanation

Solution

The large hand of the clock makes a complete revolution in 6060 minutes. \therefore Angle traced out by the large hand in 2020 minutes (of time) =360×2060=120=120π180=\frac{360^{\circ} \times 20}{60}=120^{\circ}=\frac{120\,\pi}{180} radian =2π3=\frac{2\pi}{3} radian Hence, the distance moved by the extremity of the large hand =(42)×2π3=88cm=\left(42\right)\times\frac{2\pi}{3}=88\,cm. (l=rθ)\quad\left(\because l=r\theta\right)