Question

Dacă sin(x) = -5/13 si x apartine 4 calculati cos x , tg x

Answer 1

   
In cadranul 4, sinusul este negativ, cosinusul este pozitiv si tangenta negativa.


[tex]\displaystyle \\ \sin x = \boxed{- \frac{5}{13}} \ \textless \ 0 \\ \\ \\ \cos x = \sqrt{1 - \sin^2x} = \sqrt{1 - \Big(- \frac{5}{13} \Big)^2} = \sqrt{1 - \frac{5^2}{13^2} } = \\ \\ \\ = \sqrt{ \frac{13^2 - 5^2}{13^2} } =\sqrt{ \frac{169 - 25}{13^2} } =\sqrt{ \frac{144}{13^2} } =\sqrt{ \frac{12^2}{13^2} } = \boxed{\frac{12}{13} } \ \textgreater \ 0\\ \\ \\ \text{tg } x = \frac{\sin x}{\cos x}= \frac{- \frac{5}{13}}{\frac{12}{13} }= - \frac{5}{13}\times \frac{13}{12} = \boxed{ - \frac{5}{12}} \ \textless \ 0[/tex]