[tex]sin \frac{7\pi}{6} =sin \frac{6\pi+\pi}{6}=sin(\pi+ \frac{\pi}{6})=\\
=sin\pi\cdot cos \frac{\pi}{6}+sin \frac{\pi}{6}\cdot cos \pi=\\
=- \frac{1}{2} \\
cos \frac{2\pi}{3} =cos\frac{3\pi-\pi}{3}=cos(\pi-\frac{\pi}{3})=\\
=cos\pi\cdot cos\frac{\pi}{3}+sin\pi\cdot sin \frac{\pi}{3}=\\
=- \frac{1}{2} \\
sin \frac{7\pi}{6} +cos \frac{2\pi}{3}=- \frac{1}{2} - \frac{1}{2} =-1[/tex]
