Solve {l}{sina=1/sqrt{5}}{cosbeta=-3/sqrt{10}}

$$\left. \begin{array} { l } { \sin a = \frac { 1 } { \sqrt { 5 } } } \\ { \cos \beta = - \frac { 3 } { \sqrt { 10 } } } \end{array} \right.$$

Solve for a, β

$$a=2\pi n_{1}+\arcsin(\frac{\sqrt{5}}{5})\text{, }n_{1}\in \mathrm{Z}\text{, }\beta =2\pi n_{3}-\arccos(\frac{3\sqrt{10}}{10})+\pi \text{, }n_{3}\in \mathrm{Z}$$

$$a=2\pi n_{1}+\arcsin(\frac{\sqrt{5}}{5})\text{, }n_{1}\in \mathrm{Z}\text{, }\beta =2\pi n_{4}+\arccos(\frac{3\sqrt{10}}{10})+\pi \text{, }n_{4}\in \mathrm{Z}$$

$$a=2\pi n_{2}-\arcsin(\frac{\sqrt{5}}{5})+\pi \text{, }n_{2}\in \mathrm{Z}\text{, }\beta =2\pi n_{3}-\arccos(\frac{3\sqrt{10}}{10})+\pi \text{, }n_{3}\in \mathrm{Z}$$

$$a=2\pi n_{2}-\arcsin(\frac{\sqrt{5}}{5})+\pi \text{, }n_{2}\in \mathrm{Z}\text{, }\beta =2\pi n_{4}+\arccos(\frac{3\sqrt{10}}{10})+\pi \text{, }n_{4}\in \mathrm{Z}$$