Ok i solved these problems.

a) $\displaystyle sin(arcsin(-\frac{1}{2}))$

$\displaystyle -\frac{1}{2}$ belongs to interval $\displaystyle [-\frac{\pi}{2]}, \frac{\pi}{2]}]$

so solution is $\displaystyle -\frac{1}{2}$

b) $\displaystyle arcsin(sin(\frac{7\pi}{6})$

$\displaystyle \frac{7\pi}{6}$ belongs to interval $\displaystyle \Re$

so solution is $\displaystyle \frac{7\pi}{6}$

c) $\displaystyle tg(arctg(-1))$

-1 belongs to $\displaystyle /Re $

so solution is -1