Question

cunoscând unul dintre numerele sin x, cos x, Tg x, ctg x, calculați celelalte trei numere dacă: sin x=0,6 ; x aparține (0, pi/2)​

Answer 1

$sinx = 0.6 = \frac{6}{10} = \frac{3}{5}$

$x \: \in \: (0, \frac{\pi}{2} )$

$x \: \in \: (0, \frac{\pi}{2} ) = > cadranul \: I$

${sin}^{2} x + {cos}^{2} x = 1$

${( \frac{3}{5} )}^{2} + {cos}^{2} x = 1$

$\frac{9}{25} + {cos}^{2} x = 1$

${cos}^{2} x = 1 - \frac{9}{25}$

${cos}^{2} x = \frac{16}{25}$

$cosx = \pm \sqrt{ \frac{16}{25} } = \pm \frac{4}{5}$

$x \: \in \: (0, \frac{\pi}{2} ) = > cosx > 0 = > cosx = \frac{4}{5}$

$tgx = \frac{sinx}{cosx} = \frac{ \frac{3}{5} }{ \frac{4}{5} } = \frac{3}{4}$

$ctgx = \frac{cosx}{sinx} = \frac{ \frac{4}{5} }{ \frac{3}{5} } = \frac{4}{3}$

$sau \: ctgx = \frac{1}{tgx} = \frac{1}{ \frac{3}{4} } = \frac{4}{3}$