ГДЗ по геометрии 8 класс Атанасян Задание 1013

\[\boxed{\mathbf{1013.ОК\ ГДЗ - домашка\ на}\ 5}\]

\[\textbf{а)}\ cos\ \alpha = \frac{1}{2}:\]

\[\text{si}n^{2}\alpha + cos^{2}\alpha = 1\]

\[\text{si}n^{2}\alpha = 1 - cos^{2}\alpha = 1 - \frac{1}{4} = \frac{3}{4}\]

\[sin\ \alpha = \pm \frac{\sqrt{3}}{2}.\]

\[\textbf{б)}\ cos\ \alpha = - \frac{2}{3}:\]

\[\text{si}n^{2}\alpha + cos^{2}\alpha = 1\]

\[\text{si}n^{2}\alpha = 1 - cos^{2}\alpha = 1 - \frac{4}{9} = \frac{5}{9}\]

\[sin\ \alpha = \pm \frac{\sqrt{5}}{3}.\]

\[\textbf{в)}\ cos\ \alpha = - 1:\]

\[\text{si}n^{2}\alpha + cos^{2}\alpha = 1\]

\[\text{si}n^{2}\alpha = 1 - cos^{2}\alpha = 1 - 1 =\]

\[0 = sin\ \alpha = 0.\]