Find the angle in radians through which a pendulum swings if its length is $75 \, cm$ and the tip describes an arc of length $10 \, cm$.

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:

Which of the following relations is possible?

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

$\sin 690^{\circ} \times \sec 240^{\circ} = $

$\frac{1-2(\cos 60^{\circ}-\cos 80^{\circ})}{2 \sin 10^{\circ}} = \dots$