[tex]sinx = 0.6 = \frac{6}{10} = \frac{3}{5} [/tex]
[tex]x \: \in \: (0, \frac{\pi}{2} )[/tex]
[tex]x \: \in \: (0, \frac{\pi}{2} ) = > cadranul \: I[/tex]
[tex] {sin}^{2} x + {cos}^{2} x = 1[/tex]
[tex] {( \frac{3}{5} )}^{2} + {cos}^{2} x = 1[/tex]
[tex] \frac{9}{25} + {cos}^{2} x = 1[/tex]
[tex] {cos}^{2} x = 1 - \frac{9}{25} [/tex]
[tex] {cos}^{2} x = \frac{16}{25} [/tex]
[tex]cosx = \pm \sqrt{ \frac{16}{25} } = \pm \frac{4}{5} [/tex]
[tex]x \: \in \: (0, \frac{\pi}{2} ) = > cosx > 0 = > cosx = \frac{4}{5} [/tex]
[tex]tgx = \frac{sinx}{cosx} = \frac{ \frac{3}{5} }{ \frac{4}{5} } = \frac{3}{4} [/tex]
[tex]ctgx = \frac{cosx}{sinx} = \frac{ \frac{4}{5} }{ \frac{3}{5} } = \frac{4}{3} [/tex]
[tex]sau \: ctgx = \frac{1}{tgx} = \frac{1}{ \frac{3}{4} } = \frac{4}{3} [/tex]
