Question

Se sen x=8/9
Cosx e tgx é igual a?

Answer 1

${( \sin(x)) }^{2} + {( \cos(x) )}^{2} = 1 \\ {( \frac{8}{9} )}^{2} + {( \cos(x) )}^{2} = 1 \\ {( \cos(x) )}^{2} = 1 - {( \frac{8}{9} )}^{2} \\ {( \cos(x) )}^{2} = 1 - \frac{64}{81} \\ {( \cos(x) )}^{2} = \frac{81 - 64}{81} \\ {( \cos(x) )}^{2} \\ = \frac{17}{81} \\ \cos(x) = \sqrt[2]{( \frac{17}{81} )} \\ \cos(x) = \frac{ \sqrt{17} }{9}$
$\tan(x) = \frac{ \sin(x) }{ \cos(x) } = \\ = \frac{ \frac{8}{9} }{ \frac{ \sqrt{17} }{9} } = \\ = \frac{8}{ \sqrt{17} } = \frac{8 \sqrt{17} }{17}$