Решебник по алгебре и начала математического анализа 10 класс Колягин Задание 1079

\[\boxed{\mathbf{1079}\mathbf{.}}\]

\[1)\ tg\frac{5\pi}{4} = tg\left( \pi + \frac{\pi}{4} \right) =\]

\[= \text{tg}\left( \frac{\pi}{4} \right) = 1\]

\[2)\sin\frac{7\pi}{6} = \sin\left( \pi + \frac{\pi}{6} \right) =\]

\[= - \sin\frac{\pi}{6} = - \frac{1}{2}\]

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

\[= \cos\left( - \frac{\pi}{3} \right) = \cos\frac{\pi}{3} = \frac{1}{2}\]

\[4)\ ctg\frac{5\pi}{3} = ctg\left( 2\pi - \frac{\pi}{3} \right) =\]

\[= \text{ctg}\left( - \frac{\pi}{3} \right) = - ctg\frac{\pi}{3} = - \frac{\sqrt{3}}{3}\]

\[5)\sin\left( - \frac{13\pi}{6} \right) =\]

\[= \sin\left( - 2\pi - \frac{\pi}{6} \right) = \sin\left( - \frac{\pi}{6} \right) =\]

\[= - \sin\frac{\pi}{6} = - \frac{1}{2}\]

\[6)\cos\left( - \frac{7\pi}{3} \right) =\]

\[= \cos\left( - 2\pi - \frac{\pi}{3} \right) = \cos\left( - \frac{\pi}{3} \right) =\]

\[= \cos\frac{\pi}{3} = \frac{1}{2}\]

\[7)\ tg\left( - \frac{2\pi}{3} \right) = tg\left( - \pi + \frac{\pi}{3} \right) =\]

\[= \text{tg}\frac{\pi}{3} = \sqrt{3}\]

\[8)\ ctg\left( - \frac{7\pi}{4} \right) =\]

\[= \text{ctg}\left( - 2\pi + \frac{\pi}{4} \right) = ctg\frac{\pi}{4} = 1\]