Решебник по алгебре и начала математического анализа 11 класс Колягин Задание 38

\[1)\cos\frac{\pi}{5}\ и\ \sin\frac{\pi}{5}\]

\[\sin\frac{\pi}{5} = \cos\left( \frac{\pi}{2} - \frac{\pi}{5} \right) = \cos\frac{3\pi}{10};\]

\[\cos\frac{\pi}{5} = \cos\frac{2\pi}{10} > \cos\frac{3\pi}{10};\]

\[\cos\frac{\pi}{5} > \sin\frac{\pi}{5}.\]

\[2)\sin\frac{\pi}{7}\ и\ \cos\frac{\pi}{7}\]

\[\sin\frac{\pi}{7} = \cos\left( \frac{\pi}{2} - \frac{\pi}{7} \right) = \cos\frac{5\pi}{14};\]

\[\cos\frac{\pi}{7} = \cos\frac{2\pi}{14} > \cos\frac{5\pi}{14};\]

\[\sin\frac{\pi}{7} < \cos\frac{\pi}{7}.\]

\[3)\cos\frac{3\pi}{8}\ и\ \sin\frac{5\pi}{8}\]

\[\sin\frac{5\pi}{8} = \sin\left( \frac{\pi}{2} + \frac{\pi}{8} \right) = \cos\frac{\pi}{8};\]

\[\cos\frac{3\pi}{8} < \cos\frac{\pi}{8};\]

\[\cos\frac{3\pi}{8} < \sin\frac{5\pi}{8}.\]

\[4)\sin\frac{3\pi}{5}\ и\ \cos\frac{\pi}{5}\]

\[\sin\frac{3\pi}{5} = \sin\left( \frac{\pi}{2} + \frac{\pi}{10} \right) = \cos\frac{\pi}{10};\]

\[\cos\frac{\pi}{5} = \cos\frac{2\pi}{10} < \cos\frac{\pi}{10};\]

\[\sin\frac{3\pi}{5} > \cos\frac{\pi}{5}.\]

\[5)\cos\frac{\pi}{6}\ и\ \sin\frac{5\pi}{14}\]

\[\sin\frac{5\pi}{14} = \cos\left( \frac{\pi}{2} - \frac{5\pi}{14} \right) = \cos\frac{\pi}{7};\]

\[\cos\frac{\pi}{6} < \cos\frac{\pi}{7};\]

\[\cos\frac{\pi}{6} < \sin\frac{5\pi}{14}.\]

\[6)\cos\frac{\pi}{8}\ и\ \sin\frac{3\pi}{10}\]

\[\sin\frac{3\pi}{10} = \cos\left( \frac{\pi}{2} - \frac{3\pi}{10} \right) = \frac{\pi}{5};\]

\[\cos\frac{\pi}{8} > \cos\frac{\pi}{5};\]

\[\cos\frac{\pi}{8} > \sin\frac{3\pi}{10}.\]