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

If $a = \sin 175^{\circ} + \cos 175^{\circ}$,then

If $x \cos \theta = y \cos \left(\theta + \frac{2 \pi}{3}\right) = z \cos \left(\theta + \frac{4 \pi}{3}\right)$,then $\frac{1}{x} + \frac{1}{y} + \frac{1}{z} = $

The expression $\frac{\tan \left( \frac{3\pi}{2} - \alpha \right) \cos \left( \frac{3\pi}{2} - \alpha \right)}{\cos (2\pi - \alpha )} + \cos \left( \alpha - \frac{\pi}{2} \right) \sin (\pi - \alpha ) + \cos (\pi + \alpha ) \sin \left( \alpha - \frac{\pi}{2} \right)$ when simplified reduces to:

$A$ wire of length $44 \text{ cm}$ is bent into an arc of a circle of radius $12 \text{ cm}$. The angle (in degrees) subtended by the arc at the centre of the circle is

Find the value of the trigonometric function $\sin 765^{\circ}$.