Question

Найдите значение cost, tga, ctga, если sina= 5/13

Answer 1

Ответ:

$\sin(a) = \frac{5}{13} \\ \frac{\pi}{2} < a < \pi \\ \cos(a) = \sqrt{1 - \sin^{2} (a) } = \sqrt{1 - { (\frac{5}{13})}^{2} } = \\ \sqrt{1 - \frac{25}{169} } = \sqrt{ \frac{169}{169} - \frac{25}{169} } = \sqrt{ \frac{144}{169} } = \frac{12}{13} \\ \tg(a) = \frac{ \sin(a) }{ \cos(a) } = \frac{5}{13} \div \frac{12}{13} = \frac{5}{13} \times \frac{13}{12} = \frac{5}{12} \\ \ctg(a) = \frac{1}{ \tg(a)} = 1 \div \frac{5}{12} = 1 \times \frac{12}{5} = \frac{12}{5} = 2 \frac{2}{5}$