[tex] \sin\alpha = \frac{2}{3} \\ \\ {sin}^{2} \alpha + {cos}^{2} \alpha = 1 \\ \\ {cos}^{2} \alpha = 1 - {sin}^{2} \alpha \\ \\ {cos}^{2} \alpha = 1 - \frac{4}{9} \\ \\ {cos}^{2} \alpha = \frac{5}{9} \rightarrow cos \alpha = \frac{ \sqrt{5} }{3} \\ \\ tg \alpha = \frac{sin \alpha }{cos \alpha } \\ \\ tg \alpha = \frac{ \frac{2}{3} }{ \frac{ \sqrt{5} }{3} } \\ \\ tg \alpha = \frac{2}{ \sqrt{5} } = \frac{2 \sqrt{5} }{5} \\ [/tex]
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[tex] \sin\alpha = \frac{2}{3} \\ \\ {sin}^{2} \alpha + {cos}^{2} \alpha = 1 \\ \\ {cos}^{2} \alpha = 1 - {sin}^{2} \alpha \\ \\ {cos}^{2} \alpha = 1 - \frac{4}{9} \\ \\ {cos}^{2} \alpha = \frac{5}{9} \rightarrow cos \alpha = \frac{ \sqrt{5} }{3} \\ \\ tg \alpha = \frac{sin \alpha }{cos \alpha } \\ \\ tg \alpha = \frac{ \frac{2}{3} }{ \frac{ \sqrt{5} }{3} } \\ \\ tg \alpha = \frac{2}{ \sqrt{5} } = \frac{2 \sqrt{5} }{5} \\ [/tex]