Question

ajude-me!!! exercicio pra amanha me ajudem ​

Answer 1

$\csc( \alpha ) = \frac{10}{3} \\ \sin( \alpha ) = \frac{3}{10}$

${ \cot}^{2} \alpha = { \csc}^{2} \alpha - 1 \\ \cot( \alpha ) = - \sqrt{ { \csc }^{2} \alpha - 1}$

$\cot( \alpha ) = - \sqrt{ {( \frac{10}{3} )}^{2} - 1 } \\ \cot( \alpha ) = - \sqrt{ \frac{100}{9}-1}$

$\cot( \alpha ) = - \sqrt{ \frac{100 - 9}{9} } = - \sqrt{ \frac{91}{9} } \\ \cot( \alpha ) = - \frac{ \sqrt{91} }{3}$

$\tan( \alpha ) = - \frac{3}{ \sqrt{91} } = - \frac{3 \sqrt{91} }{91}$

$\cos( \alpha ) = \frac{ \sin( \alpha ) }{ \tan( \alpha ) } \\ \cos( \alpha ) = \frac{ \frac{3}{10} }{ - \frac{3 \sqrt{91} }{91} }$

$\cos( \alpha ) = \frac{3}{10}. \frac{ - 91}{3 \sqrt{91} } = - \frac{91}{10 \sqrt{91 } } \\ \cos( \alpha) = - \frac{91 \sqrt{91} }{10.91} = - \frac{ \sqrt{91} }{10}$

$\sec( \alpha ) = - \frac{10 \sqrt{91} }{91}$