Question

1) Sa se calculeze cosx, tg x, ctg x, daca x apartine ( 0, pi) si sin x = 3 /5

2) Sa se calculeze sin 2x, daca x apartine ( pi / 2, pi) si cos x = - 12 /13

Answer 1

1.Aflăm cât este cosx întâi de toate.
$cos^{2} x+sin ^{2} x=1 =\ \textgreater \ cos^{2} x=1-sin ^{2} x =\ \textgreater \ cosx= \sqrt{1- sin^{2}x }$ $cosx= \sqrt{1- \frac{9}{25} } = \sqrt{ \frac{16}{25} } = \frac{4}{5}$
$tgx= \frac{sinx}{cosx} = \frac{ \frac{3}{5} }{ \frac{4}{5} } = \frac{3}{4}$

$ctgx= \frac{cosx}{sinx} = \frac{ \frac{4}{5} }{ \frac{3}{5} } = \frac{4}{3}$
2.  sin2x=2sinxcosx
aflam sinx
$sinx= \sqrt{1- \frac{144}{169} } = \sqrt{ \frac{169-144}{169} } = \sqrt{ \frac{25}{169} } = \frac{5}{13}$
$sin2x=2sinxcosx=2* \frac{5}{13} * \frac{-12}{13} = \frac{-120}{169}$