Question

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

Answer 1

Ответ:

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

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

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

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

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