Question

Найдите sinα, tgα и ctgα, если cosα=1/4

Answer 1

Ответ:

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

$\sin( \alpha ) = \sqrt{1 - ( { \frac{1}{4} )}^{2} } = \\ \sqrt{1 - \frac{1}{16} } = \sqrt{ \frac{15}{16} } = \frac{ \sqrt{15} }{4}$

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

$\cot( \alpha ) = \frac{ \frac{ \frac{1}{4} }{ \sqrt{15} } }{4} = \frac{1}{4} \times \frac{4}{ \sqrt{15} } = \\ = \frac{1}{ \sqrt{15} } = \frac{ \sqrt{15} }{15}$

$\ \tan( \alpha ) = \frac{1}{ \ \cot ( \alpha ) } = \frac{ \frac{1}{1} }{ \sqrt{15} } = \\ = 1 \times \sqrt{15} = \sqrt{15}$