Решебник по алгебре и начала математического анализа 10 класс Колягин Задание 1142

\[\boxed{\mathbf{1142}\mathbf{.}}\]

\[OC = R = 200;\ \ OC_{1} = R -\]

\[- 2OA_{1} = 200 - 4 = 196.\]

\[\cos a = \frac{OC_{1}}{R} = \frac{196}{200} = \frac{98}{100} =\]

\[= 0,98 \rightarrow a \approx 1,816875.\]

\[l = 2 \cdot (2aR + CB) =\]

\[= 2 \cdot (2 \cdot 1,816875 \cdot 200 + 4) =\]

\[= 1461,5\ м.\]

\[Ответ:1461,5\ м.\]

\[\boxed{\mathbf{1143}\mathbf{.}}\]

\[1)\arccos 0 = \frac{\pi}{2}\]

\[2)\arccos 1 = 0\]

\[3)\arccos\frac{\sqrt{2}}{2} = \frac{\pi}{4}\]

\[4)\arccos\frac{1}{2} = \frac{\pi}{3}\]

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

\[- \arccos\frac{\sqrt{3}}{2} = \pi - \frac{\pi}{6} = \frac{5\pi}{3}\]

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

\[- \arccos\frac{\sqrt{2}}{2} = \pi - \frac{\pi}{4} = \frac{3\pi}{4}\]