A circular wire of radius $7\,cm$ is cut and bend again into an arc of a circle of radius $12\,cm$. The angle subtended by the arc at the centre is ......$^o$

If $A + B + C = \pi $ and $\cos A = \cos B\,\cos C,$ then $\tan B\,\,\tan C$ is equal to

Find the radius of the circle in which a central angle of $60^{\circ}$ intercepts an arc of length $37.4 \,cm$ ( use $\pi=\frac{22}{7}$ ).

Find the value of the trigonometric function $\tan \frac{19 \pi}{3}$.

Find the angle in radian through which a pendulum swings if its length is $75\, cm$ and the tip describes an arc of length.

$10 \,cm$

If $\theta $ and $\phi $ are angles in the $1^{st}$ quadrant such that $\tan \theta = 1/7$ and $\sin \phi = 1/\sqrt {10} $.Then