\[1)\sin{150{^\circ}} = \sin(90{^\circ} + 60{^\circ}) =\]
\[= \cos{60{^\circ}} = \frac{1}{2};\]
\[2)\cos{150{^\circ}} = \cos(90{^\circ} + 60{^\circ}) =\]
\[= - \sin{60{^\circ}} = - \frac{\sqrt{3}}{2};\]
\[3)\ tg\ 150{^\circ} = \frac{\sin{150{^\circ}}}{\cos{150{^\circ}}} =\]
\[= \frac{1}{2}\ :\left( - \frac{\sqrt{3}}{2} \right) = - \frac{1}{\sqrt{3}};\]
\[4)\ ctg\ 150{^\circ} = \frac{1}{tg\ 150{^\circ}} = - \sqrt{3}.\]