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

Find the values of the other five trigonometric functions if $\cos x = -\frac{1}{2}$ and $x$ lies in the third quadrant.

Which of the following trigonometric values are negative?
$I. \sin(-292^{\circ})$
$II. \tan(-190^{\circ})$
$III. \cos(-207^{\circ})$
$IV. \cot(-222^{\circ})$

The points $(\cos \alpha, \sin \alpha)$ and $(\cos (\pi+\alpha), \sin (\pi+\alpha))$ for $\alpha \in R$ have directions:

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:

$\frac{\sin 70^\circ + \cos 40^\circ}{\cos 70^\circ + \sin 40^\circ} = $