Решебник по алгебре и начала математического анализа 10 класс Алимов Задание 735

\[\boxed{\mathbf{735}\mathbf{.}}\]

\[y = \text{tg\ x};\]

\[Возрастает\ на\ \ \]

\[\left\lbrack - \frac{\pi}{2} + \pi n;\ \frac{\pi}{2} + \pi n \right\rbrack.\]

\[1)\ tg\frac{\pi}{5}\text{\ \ }и\ \ \text{tg}\frac{\pi}{7};\]

\[\frac{\pi}{5}\ и\ \frac{\pi}{7}\ принадлежат\ \left\lbrack - \frac{\pi}{2};\ \frac{\pi}{2} \right\rbrack;\]

\[\frac{\pi}{5} > \frac{\pi}{7}\]

\[\text{tg}\frac{\pi}{5} > tg\frac{\pi}{7}.\]

\[2)\ tg\frac{7\pi}{8}\text{\ \ }и\ \ \text{tg}\frac{8\pi}{9};\]

\[\frac{7\pi}{8}\ и\ \frac{8\pi}{9}\ принадлежат\left\lbrack \frac{\pi}{2};\ \frac{3\pi}{2} \right\rbrack;\]

\[\frac{7\pi}{8} < \frac{8\pi}{9}\]

\[\text{tg}\frac{7\pi}{8} < tg\frac{8\pi}{9}.\]

\[3)\ tg\left( - \frac{7\pi}{8} \right)\ и\ \ \text{tg}\left( - \frac{8\pi}{9} \right);\]

\[- \frac{7\pi}{8}\ и\ - \frac{8\pi}{9}\ принадлежат\]

\[\left\lbrack - \frac{3\pi}{2};\ - \frac{\pi}{2} \right\rbrack;\]

\[- \frac{7\pi}{8} > - \frac{8\pi}{9}\]

\[\text{tg}\left( - \frac{7\pi}{8} \right) > tg\left( - \frac{8\pi}{9} \right).\]

\[4)\ tg\left( - \frac{\pi}{5} \right)\ и\ \ \text{tg}\left( - \frac{\pi}{7} \right);\]

\[- \frac{\pi}{5}\ и\ - \frac{\pi}{7}\ принадлежат\left\lbrack - \frac{\pi}{2};\ \frac{\pi}{2} \right\rbrack;\]

\[- \frac{\pi}{5} < - \frac{\pi}{7}\]

\[\text{tg}\left( - \frac{\pi}{5} \right) < tg\left( - \frac{\pi}{7} \right).\]

\[5)\ tg\ 2\ \ и\ \ tg\ 3;\]

\[2\ и\ 3\ принадлежат\left\lbrack \frac{\pi}{2};\ \frac{3\pi}{2} \right\rbrack;\]

\[2 < 3\]

\[tg\ 2 < tg\ 3.\]

\[6)\ tg\ 1\ \ и\ \ tg\ 1,5;\]

\[1\ и\ 1,5\ принадлежат\left\lbrack - \frac{\pi}{2};\ \frac{\pi}{2} \right\rbrack;\]

\[1 < 1,5\]

\[tg\ 1 < tg\ 1,5.\]