Решебник по алгебре и начала математического анализа 11 класс Колягин Задание 65

\[y = \sin x.\]

\[1)\ x \in \left\lbrack \frac{\pi}{6};\ \pi \right\rbrack:\]

\[y\left( \frac{\pi}{6} \right) = \sin\frac{\pi}{6} = \frac{1}{2};\]

\[y\left( \frac{\pi}{2} \right) = \sin\frac{\pi}{2} = 1;\]

\[y(\pi) = \sin\pi = 0.\]

\[E(y) = \lbrack 0;\ 1\rbrack.\]

\[2)\ x \in \left\lbrack \frac{3\pi}{4};\ \frac{5\pi}{4} \right\rbrack:\]

\[y\left( \frac{3\pi}{4} \right) = \sin\frac{3\pi}{4} = \sin\frac{\pi}{4} = \frac{\sqrt{2}}{2};\]

\[y\left( \frac{5\pi}{4} \right) = \sin\frac{5\pi}{4} = - \sin\frac{\pi}{4} = - \frac{\sqrt{2}}{2}.\]

\[E(y) = \left\lbrack - \frac{\sqrt{2}}{2};\ \frac{\sqrt{2}}{2} \right\rbrack.\]