A wheel makes ${360^\circ }$ revolutions in one minute. Through how many radians does it turn in one second?
Number of revolutions made by the wheel in $1$ minute $=360$
$\therefore$ Number of revolutions made by the wheel in $1$ second $=\frac{360}{60}=6$
In one complete revolution, the wheel turns an angle of $2 \pi$ radian.
Hence, in $6$ complete revolutions, it will turn an angle of $6 \times 2 \pi$ radian,
i.e., $12 \pi$ radian
Thus, in one second, the wheel turns an angle of $12 \pi$ radian.
If $a\,{\cos ^3}\alpha + 3a\,\cos \alpha \,{\sin ^2}\alpha = m$ and $a\,{\sin ^3}\alpha + 3a\,{\cos ^2}\alpha \sin \alpha = n,$ then ${(m + n)^{2/3}} + {(m - n)^{2/3}}$ is equal to
Find the value of $\sin 15^{\circ}$
Observe that, at any instant, the minute and hour hands of a clock make two angles between them whose sum is $360^{\circ}$. At $6: 15$ the difference between these two angles is $....^{\circ}$
In a circle of diameter $40 \,cm ,$ the length of a chord is $20 \,cm .$ Find the length of minor arc of the chord.
Find the degree measures corresponding to the following radian measures (Use $\pi=\frac{22}{7}$ ).
$\frac{11}{16}$