Решебник по алгебре и начала математического анализа 11 класс Алимов Задание 524

\[\boxed{\mathbf{524}\mathbf{.}}\]

\[1)\cos{75{^\circ}} = \cos(90{^\circ} - a)\]

\[75{^\circ} = 90{^\circ} - a\]

\[a = 90{^\circ} - 75{^\circ} = 15{^\circ}\]

\[Ответ:\ \ 15{^\circ}.\]

\[2)\sin{150{^\circ}} = \sin(90{^\circ} + a)\]

\[150{^\circ} = 90{^\circ} + a\]

\[a = 150{^\circ} - 90{^\circ} = 60{^\circ}\]

\[Ответ:\ \ 60{^\circ}.\]

\[3)\sin{150{^\circ}} = \sin(180{^\circ} - a)\]

\[150{^\circ} = 180{^\circ} - a\]

\[a = 180{^\circ} - 150{^\circ} = 30{^\circ}\]

\[Ответ:\ \ 30{^\circ}.\]

\[4)\cos{310{^\circ}} = \cos(270{^\circ} + a)\]

\[310{^\circ} = 270{^\circ} + a\]

\[a = 310{^\circ} - 270{^\circ} = 40{^\circ}\]

\[Ответ:\ \ 40{^\circ}.\]

\[5)\sin\frac{5\pi}{4} = \sin(\pi + a)\]

\[\frac{5\pi}{4} = \pi + a\]

\[a = \frac{5\pi}{4} - \pi = \frac{5\pi}{4} - \frac{4\pi}{4} = \frac{\pi}{4}\]

\[Ответ:\ \ \frac{\pi}{4}\]

\[6)\ tg\frac{\pi}{5} = tg\left( \frac{\pi}{2} - a \right)\]

\[\frac{\pi}{5} = \frac{\pi}{2} - a\]

\[a = \frac{\pi}{2} - \frac{\pi}{5} = \frac{5\pi}{10} - \frac{2\pi}{10} = \frac{3\pi}{10}\]

\[Ответ:\ \ \frac{3\pi}{10}.\]

\[7)\cos\frac{7\pi}{4} = \cos\left( \frac{3\pi}{2} + a \right)\]

\[\frac{7\pi}{4} = \frac{3\pi}{2} + a\]

\[a = \frac{7\pi}{4} - \frac{3\pi}{2} = \frac{7\pi}{4} - \frac{6\pi}{4} = \frac{\pi}{4}\]

\[Ответ:\ \ \frac{\pi}{4}.\]

\[8)\ ctg\frac{11\pi}{6} = ctg(2\pi - a)\]

\[\frac{11\pi}{6} = 2\pi - a\]

\[a = 2\pi - \frac{11\pi}{6} = \frac{12\pi}{6} - \frac{11\pi}{6} = \frac{\pi}{6}\]

\[Ответ:\ \ \frac{\pi}{6}.\]