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Q.
The minute hand of a watch is $1.5 \,cm$ long. How far does its tip move in $40$ minutes? (Use $\pi = 3.14$)
Trigonometric Functions
Solution:
In $60$ minutes, the minute hand of a watch completes one revolution. Therefore, in $40$ minutes, the minute hand turns through $\frac{2}{3}$ of a revolution. Therefore $\theta=\frac{2}{3} \times 360^{\circ}$ or $\frac{4\pi}{3}$ radian. Hence, the required distance travelled is given by
$l=r\theta=1.5 \times \frac{4\pi}{3}$
$=2\pi=2\times 3.14=6.28\,cm$.