\[\boxed{\mathbf{1018.ОК\ ГДЗ - домашка\ на}\ 5}\]
\[Рисунок\ по\ условию\ задачи:\]
\[\mathbf{Дано:}\]
\[\textbf{а)}\ OA = 3;\ \alpha = 45{^\circ};\]
\[\textbf{б)}\ OA = 1,5;\ \alpha = 90{^\circ};\]
\[\textbf{в)}\ OA = 5;\ \alpha = 150{^\circ};\]
\[\textbf{г)}\ OA = 1;\ \alpha = 180{^\circ};\]
\[\textbf{д)}\ OA = 2;\ \alpha = 30{^\circ}.\]
\[\mathbf{Найти:}\]
\[A(x;y) - ?\]
\[\mathbf{Решение.}\]
\[1)\ Вычисление\ координат\ \]
\[точки\ A:\]
\[x = OA \bullet \cos\alpha;\ \ \ y = OA \bullet \sin\alpha.\]
\[\textbf{а)}\sin{45{^\circ}} = \frac{\sqrt{2}}{2};\cos{45{^\circ}} = \frac{\sqrt{2}}{2}.\]
\[\textbf{б)}\sin{90{^\circ}} = 1;\cos{90{^\circ}} = 0.\]
\[\left\{ \begin{matrix} x = 1,5 \bullet 0 = 0\ \ \ \\ y = 1,5 \bullet 1 = 1,5 \\ \end{matrix} \right.\ \Longrightarrow A(0;1,5).\]
\[\textbf{в)}\sin{150{^\circ}} = \frac{1}{2};\]
\[\cos{150{^\circ}} = - \frac{\sqrt{3}}{2}.\]
\[\textbf{г)}\sin{180{^\circ}} = 0;\cos{180{^\circ}} = - 1.\]
\[\left\{ \begin{matrix} x = 1 \bullet ( - 1) = - 1 \\ y = 1 \bullet 0 = 0\ \ \ \ \ \ \ \ \ \ \\ \end{matrix} \right.\ \Longrightarrow A( - 1;0).\]
\[\textbf{д)}\sin{30{^\circ}} = \frac{1}{2};\cos{30{^\circ}} = \frac{\sqrt{3}}{2}.\]
\[\left\{ \begin{matrix} x = 2 \bullet \frac{\sqrt{3}}{2} = \sqrt{3} \\ y = 2 \bullet \frac{1}{2} = 1\ \ \ \ \ \\ \end{matrix} \right.\ \Longrightarrow A\left( \sqrt{3};1 \right).\]
\[Ответ:а)\ A\left( \frac{3\sqrt{2}}{2};\frac{3\sqrt{2}}{2} \right);\ \]
\[\ \ \ \ \ \ \ \ \ \ \ \ \ \ б)\ A(0;1,5);\ \]
\[\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ в)\ A\left( - \frac{5\sqrt{3}}{2};\frac{5}{2} \right);\]
\[\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ г)\ A( - 1;0);\ \]
\[\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ д)\ A(\sqrt{3};1).\]
\[\boxed{\mathbf{1018.еуроки - ответы\ на\ пятёрку}}\]
\[Рисунок\ по\ условию\ задачи:\]
\[\mathbf{Дано:}\]
\[MNPQ - квадрат;\]
\[\text{P\ }( - 3;3);\]
\[PM \cap NQ = (0;0).\]
\[\mathbf{Найти:}\]
\[координаты\ Q\ ,M\ и\ \text{N.}\]
\[\mathbf{Решение.}\]
\[Задача\ имеет\ два\ решения\ \]
\[в\ зависимости\ от\ обозначения\ \]
\[квадрата:\]
\[1)\ P\ ( - 3;3);Q\ (3;3);M\ (3;\ - 3);\]
\[\text{N\ }(\ - 3; - 3).\]
\[2)\ P\ ( - 3;3);Q\ ( - 3; - 3);\]
\[\text{M\ }(3;\ - 3);N\ (\ 3;3).\]