ГДЗ по геометрии 8 класс Атанасян Задание 1017

\[\boxed{\mathbf{1017.ОК\ ГДЗ - домашка\ на}\ 5}\]

\[\textbf{а)}\sin{\angle A} = \frac{2}{3}.\]

\[Начертим\ единичную\ \]

\[окружность:\]

\[2)\ sin^{2}\angle A + cos^{2\ }\angle A = 1;\]

\[\left( \frac{2}{3} \right)^{2} + cos^{2}\angle A = 1\]

\[\text{co}s^{2}\angle A = 1 - \frac{4}{9} = \frac{5}{9}\]

\[\cos{\angle A} = \frac{\sqrt{5}}{3} \approx 0,75.\]

\[x_{M} = 0,75;\ \ y_{M} = \frac{2}{3}.\]

\[\textbf{б)}\cos{\angle A} = \frac{3}{4}.\]

\[Начертим\ единичную\ \]

\[окружность.\]

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

\[\sin^{2}\angle A + \left( \frac{3}{4} \right)^{2} = 1\]

\[\sin^{2}{\angle A} = 1 - \frac{9}{16} = \frac{7}{16}\]

\[\sin{\angle A} = \frac{\sqrt{7}}{4} \approx 0,66 \approx \frac{2}{3}.\]

\[x_{M} = \frac{2}{3};y_{M} = \frac{3}{4}.\]

\[\textbf{в)}\cos{\angle A} = - \frac{2}{5};\]

\[Начертим\ единичную\ \]

\[окружность.\]

\[\text{si}n^{2}\angle A + cos^{2\ }\angle A = 1;\]

\[\sin^{2}\angle A + \left( - \frac{2}{5} \right)^{2} = 1\]

\[\sin^{2}{\angle A} = 1 - \frac{4}{25} = \frac{21}{25}\]

\[\sin{\angle A} = \frac{\sqrt{21}}{5} \approx 0,91.\]

\[x_{M} = - \frac{2}{5};y_{M} = 0,91.\]