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

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Find the values of the other five trigonometric functions if $\sec x = \frac{13}{5}$ and $x$ lies in the fourth quadrant.

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If $\sin \left( x + \frac{4\pi}{9} \right) = a$ and $\frac{\pi}{9} < x < \frac{\pi}{3}$,then $\cos \left( x + \frac{7\pi}{9} \right)$ equals:

If $\sec \theta = \frac{13}{12}$ and $\theta$ lies in the $4^{\text{th}}$ quadrant,then $\tan \theta \times \operatorname{cosec} \theta \times \sin \theta \times \cos \theta = $

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