Explicație pas cu pas:
[tex] \cos(x) = \frac{1}{3} ; \: x \in \left(0 ; \frac{\pi}{2} \right) \\ [/tex]
[tex]\sin^{2} (x) + \cos^{2} (x) = 1[/tex]
[tex]\sin^{2} (x) = 1 - \left(\frac{1}{3} \right)^{2} = 1 - \frac{1}{9} = \frac{8}{9} \\ = > \sin(x) = \frac{2 \sqrt{2} }{3}[/tex]
[tex] \tg(x) = \frac{ \sin(x) }{ \cos(x) } = \frac{ \frac{2 \sqrt{2} }{3} }{ \frac{1}{3} } \\ = > \tg(x) = 2 \sqrt{2} [/tex]
[tex]\ctg(x) = \frac{ \cos(x) }{ \sin(x) } = \frac{ \frac{1}{3} }{ \frac{2 \sqrt{2} }{3} } = \frac{1}{2 \sqrt{2} } \\ = > \ctg(x) = \frac{ \sqrt{2} }{4}[/tex]
