Find the degree measure of the angle subtended at the centre of a circle of radius $100 \,cm$ by an arc of length $22\, cm$ ( Use $\pi=\frac{22}{7}$ ).
We know that in a circle of radius $r$ unit, if an are of length $l$ unit subtends an angle $\theta$ radian at the centre, then
$\theta=\frac{1}{r}$
Therefore, for $r=100 \,cm , l=22 \,cm ,$ we have
$\theta=\frac{22}{100}$ radian
$=\frac{180}{\pi} \times \frac{22}{100}$ degree
$=\frac{180 \times 7 \times 22}{22 \times 100}$ degree
$=\frac{126}{10}$ degree
$=12 \frac{3}{5}$ degree
$=12^{\circ} 36^{\prime} \quad \quad\left[1^{\circ}=60^{\prime}\right]$
Thus, the required angle is $12^{\circ} 36^{\prime}$
If $\sin \theta + {\rm{cosec}}\theta = 2,$ the value of ${\sin ^{10}}\theta + {\rm{cose}}{{\rm{c}}^{10}}\theta $ is
The minute hand of a watch is $1.5 \,cm$ long. How far does its tip move in $40$ minutes? ( Use $\pi=3.14$ ).
Find the radian measures corresponding to the following degree measures:
$240^{\circ}$
If $0 < x < \pi $ and $\cos x + \sin x = \frac{1}{2}$,then $tan \,x$ is
The equation ${\sec ^2}\theta = \frac{{4xy}}{{{{(x + y)}^2}}}$ is only possible when