Question

найдите tg a, ctg a если sin a =1/3​

Answer 1

Ответ:

$\sin ^{2} ( \alpha ) + \cos^{2}( \alpha ) = 1 \\ \cos^{2}( \alpha ) = 1 - \sin^{2} ( \alpha ) \\ \cos( \alpha ) = \sqrt{1 - \sin^{2}( \alpha ) }$

$\displaystyle \cos( \alpha ) = \sqrt{1 - \bigg( \frac{1}{3} \bigg)^{2} } \\ \cos( \alpha ) = \sqrt{1 - \frac{1}{9} } \\ \cos( \alpha ) = \sqrt{ \frac{8}{9} } \\ \cos( \alpha ) = \frac{2 \sqrt{2} }{3}$

$\tan( \alpha ) = \frac{ \sin( \alpha ) }{ \cos( \alpha ) } \\ \cot( \alpha ) = \frac{ \cos( \alpha ) }{ \sin( \alpha ) } = \frac{1}{ \tan( \alpha ) }$

$\tan( \alpha ) = \frac{ \frac{1}{3} }{ \frac{2 \sqrt{2} }{3} } = \frac{1}{2 \sqrt{2} } = \frac{ \sqrt{2} }{4}$

$\cot( \alpha ) = 2 \sqrt{2}$