Question

Дано: cosa=-3/5 п<а<3п/2

Answer 1

Ответ:

$sin(\alpha) = -\frac{4}{5},\, tg(\alpha) = \frac{4}{3},\, ctg(\alpha) = \frac{3}{4}$

Пошаговое объяснение:

$cos(\alpha) = -\frac{3}{5},\,\pi<\alpha<\frac{3\pi}{2}\\\\\alpha\in(\pi;\;\frac{3\pi}{2})\Rightarrow\alpha\in III\Rightarrow sin(\alpha)<0\\\\sin(\alpha) = -\sqrt{1-cos^2(\alpha)}=-\sqrt{1-(-\frac{3}{5})^2}=-\sqrt{1-\frac{9}{25}}=-\sqrt{\frac{16}{25}} = -\frac{4}{5}\\\\tg(\alpha)=\frac{sin(\alpha)}{cos(\alpha)}=\frac{-\frac{4}{5}}{-\frac{3}{5}} = \frac{4}{3}\\\\ctg(\alpha) = \frac{cos(\alpha)}{sin(\alpha)} = \frac{1}{tg(\alpha)} =\frac{3}{4}$