Question

Вычислите значение остальных трех тригонометрических функций: cos α = - 12/13, π < α < 3π/2

Answer 1

$sina=- \sqrt{1-cos ^{2} a} = -\sqrt{1-(- \frac{12}{13})^{2} } = - \sqrt{1- \frac{144}{169} }= \\=- \sqrt{ \frac{169-144}{169} } =- \sqrt{ \frac{25}{169} } =- \frac{5}{13} \\\\tga= \frac{sina}{cosa} = \frac{- \frac{5}{13} }{- \frac{12}{13} } = \frac{5}{13} : \frac{12}{13} = \frac{5*13}{13*12} = \frac{5}{12} \\\\ctga= \frac{1}{tga} = \frac{1}{ \frac{5}{12} } = \frac{12}{5} = \frac{24}{10} =2.4$