Дано:sina=3/5 П/2<a>Пнайти: cosa tga ctga

$\frac{\pi}{2}<a<\pi$ значит

0; tg a<0; ctg a<0" alt="sin a>0; tg a<0; ctg a<0" align="absmiddle" class="latex-formula">

$sin^2 a+cos^2 a=1$
$cos a=-\sqrt{1-sin^2 a}=-\sqrt{1-(\frac{3}{5})^2}=-\sqrt{1-\frac{9}{25}}=\\\\-\sqrt{\frac{16}{25}}=-\frac{4}{5}$

$tg a=\frac{sin a}{cos a}=\frac{3}{5}:(-\frac{4}{5})=-\frac{3}{4}$
$ctg a=\frac{1}{tg a}=\frac{1}{-\frac{3}{4}}=-\frac{4}{3}$