The minute hand of a watch is $1.5 \,cm$ long. How far does its tip move in $40$ minutes? ( Use $\pi=3.14$ ).
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, ${\theta = 23 \times {{360}^\circ }}$ or $\frac{4 \pi}{3}$ radian. Hence, the required distance travelled is given by
$l=r \theta=1.5 \times \frac{4 \pi}{3} \,cm =2 \pi \,cm =2 \times 3.14 \,cm =6.28 \,cm$
Convert $40^{\circ} 20^{\prime}$ into radian measure.
Prove that:
$2 \sin ^{2} \frac{\pi}{6}+\cos ec ^{2} \frac{7 \pi}{6} \cos ^{2} \frac{\pi}{3}=\frac{3}{2}$
The incorrect statement is
Find the values of other five trigonometric functions if $\sin x=\frac{3}{5}, x$ lies in second quadrant.
Find the values of other five trigonometric functions if $\cos x=-\frac{1}{2}, x$ lies in third quadrant.