Решебник по алгебре и начала математического анализа 11 класс Колягин Задание 42

\[y = \cos x.\]

\[1)\ x \in \left\lbrack \frac{\pi}{3};\ \pi \right\rbrack:\]

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

\[y(\pi) = \cos\pi = - 1.\]

\[E(y) = \left\lbrack - 1;\ \frac{1}{2} \right\rbrack.\]

\[2)\ x \in \left( \frac{5\pi}{4};\ \frac{7\pi}{4} \right):\]

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

\[y\left( \frac{7\pi}{4} \right) = \cos\frac{7\pi}{4} = \cos\frac{\pi}{4} = \frac{\sqrt{2}}{2}.\]

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