$a)$  

$\alpha ={135}^{\circ }$  

 

$\sin {135}^{\circ }=\sin \left({180}^{\circ }-{45}^{\circ }\right)=\sin {45}^{\circ }=\frac{\sqrt{2}}{2}$       

$\cos {135}^{\circ }=\cos \left({180}^{\circ }-{45}^{\circ }\right)=-\cos {45}^{\circ }=-\frac{\sqrt{2}}{2}$  

$\mathrm{tg}{135}^{\circ }=\mathrm{tg}\left({180}^{\circ }-{45}^{\circ }\right)=-\mathrm{tg}{45}^{\circ }=-1$  

$\mathrm{ctg}{135}^{\circ }=\frac{1}{\mathrm{tg}{135}^{\circ }}=\frac{1}{-1}=-1$  

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$\text{b)}$  

$\alpha ={150}^o$  

 

$\sin {150}^{\circ }=\sin \left({180}^o-{30}^{\circ }\right)=\sin {30}^o=\frac{1}{2}$     

$\cos {150}^{\circ }=\cos \left({180}^{\circ }-{30}^{\circ }\right)=-\cos {30}^{\circ }=-\frac{\sqrt{3}}{2}$  

$\mathrm{tg}{150}^{\circ }=\mathrm{tg}\left({180}^{\circ }-{30}^{\circ }\right)=-\mathrm{tg}{30}^{\circ }=-\frac{\sqrt{3}}{3}$  

$\mathrm{ctg}{150}^{\circ }=\frac{1}{\mathrm{tg}{150}^{\circ }}=\frac{1}{-\frac{\sqrt{3}}{3}}=-\frac{3}{\sqrt{3}}=-\frac{3\sqrt{3}}{3}=-\sqrt{3}$