Explicație pas cu pas:
[tex]\sin^{2} (x) + \cos^{2} (x) = 1[/tex]
[tex]sin(x) = \frac{4}{5} \\ [/tex]
[tex]\cos^{2} (x) = 1 - {\Big( \frac{4}{5} \Big)}^{2} = 1 - \frac{16}{25} = \frac{9}{25} \\ \implies \cos(x) = \pm \frac{3}{5} [/tex]
[tex]x \in \Big( \frac{\pi}{2} ;\pi \Big) \implies cadranul \: \: 2 \\ \implies \cos(x) = - \frac{3}{5} [/tex]
[tex]tg(x) = \frac{ \sin(x) }{ \cos(x) } = - \frac{ \frac{4}{5} }{\frac{3}{5} } \\ \implies tg(x) = - \frac{4}{3} [/tex]
