$a)$  

$\sin \left(\frac{\pi }{6}\right)=\sin \left(\frac{1}{6}\cdot {180}^{\circ }\right)=\sin {30}^{\circ }=\frac{1}{2}$    

 

$b)$     

$\cos \left(\frac{5}{3}\pi \right)=\cos \left(\frac{5}{3}\cdot {180}^{\circ }\right)=\cos {300}^{\circ }=\cos \left({270}^{\circ }+{30}^{\circ }\right)=\sin {30}^{\circ }=\frac{1}{2}$ $\cos \left(\frac{5}{3}\pi \right)=\cos \left(\frac{5}{3}\cdot {180}^{\circ }\right)=\cos {300}^{\circ }=\cos \left({270}^{\circ }+{30}^{\circ }\right)=\sin {30}^{\circ }=\frac{1}{2}$   

 

$c)$  

$\mathrm{tg}\left(\frac{7}{4}\pi \right)=\mathrm{tg}\left(\frac{7}{4}\cdot {180}^{\circ }\right)=\mathrm{tg}\left(7\cdot {45}^{\circ }\right)=\mathrm{tg}{315}^{\circ }=\mathrm{tg}{135}^{\circ }=\mathrm{tg}\left({90}^{\circ }+{45}^{\circ }\right)=-\mathrm{ctg}{45}^{\circ }=-1$  

 

$d)$  

$\mathrm{ctg}\left(\frac{5}{4}\pi \right)=\mathrm{ctg}\left(\frac{5}{4}\cdot {180}^{\circ }\right)=\mathrm{ctg}{225}^{\circ }=\mathrm{ctg}{45}^{\circ }=1$  

 

$e)$  

$\cos \left(\frac{2}{3}\pi \right)=\cos {120}^{\circ }=\cos \left({90}^{\circ }+{30}^{\circ }\right)=-\sin {30}^{\circ }=-\frac{1}{2}$  

 

$f)$  

$\mathrm{ctg}\left(\frac{3}{4}\pi \right)=\mathrm{ctg}{135}^{\circ }=\mathrm{ctg}\left({90}^{\circ }+{45}^{\circ }\right)=-\mathrm{tg}{45}^{\circ }=-1$  

 

$g)$  

$\mathrm{tg}\left(\frac{5}{6}\pi \right)=\mathrm{tg}\left(\frac{5}{6}\cdot {180}^{\circ }\right)=\mathrm{tg}{150}^{\circ }=\mathrm{tg}\left({90}^{\circ }+{60}^{\circ }\right)=-\mathrm{ctg}{60}^{\circ }=-\frac{\sqrt{3}}{3}$  

 

$h)$  

$\sin \left(\frac{11}{6}\pi \right)=\sin \left(\frac{11}{6}\cdot {180}^{\circ }\right)=\sin \left(11\cdot {30}^{\circ }\right)=\sin {330}^{\circ }=\sin \left({270}^{\circ }+{60}^{\circ }\right)=-\cos {60}^{\circ }=-\frac{1}{2}$