Решебник по алгебре и начала математического анализа 10 класс Колягин Задание 1077

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\[1)\sin{150{^\circ}} = \sin(90{^\circ} + a)\]

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

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

\[Ответ:\ \ 60{^\circ}.\]

\[2)\cos{310{^\circ}} = \cos(270{^\circ} + a)\]

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

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

\[Ответ:\ \ 40{^\circ}.\]

\[3)\ tg\frac{\pi}{5} = tg\left( \frac{\pi}{2} - a \right)\]

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

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

\[Ответ:\ \ \frac{3\pi}{10}.\]

\[4)\ ctg\frac{11\pi}{6} = ctg(2\pi - a)\]

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

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

\[Ответ:\ \ \frac{\pi}{6}.\]