Question

Sa se calculeze tg x stiind ca x este un unghi obtuz, iar sin x=3/5.

Answer 1

[tex] \\ sinx = \frac{3}{5} \\ cos^{2}x = 1-sin^{2}x \Rightarrow cos^{2}x = 1 - \frac{9}{25} \Rightarrow cos^{2}x= \frac{25-9}{25} \Rightarrow \\ \Rightarrow cos^{2}x=\frac{16}{25} \Rightarrow cosx = \frac{4}{5} \\ \\ tgx = \frac{sinx}{cosx} \Rightarrow tgx = \frac{ \frac{3}{5} }{ \frac{4}{5} } \Rightarrow tgx = \frac{3}{4} \\ Dar\quad x\in{[\pi,2\pi] \Rightarrow tgx = - \frac{3}{4} [/tex]