Решебник по алгебре и начала математического анализа 11 класс Колягин Задание 30

\[y = \cos^{2}x;\ \ \ x = a.\]

\[1)\ a = \frac{\pi}{4}:\]

\[\cos^{2}\frac{\pi}{4} = \left( \frac{\sqrt{2}}{2} \right)^{2} = \frac{2}{4} = \frac{1}{2};\]

\[2)\ a = \frac{\pi}{2}:\]

\[\cos^{2}\frac{\pi}{2} = 0^{2} = 0;\]

\[3)\ a = \frac{2\pi}{3}:\]

\[\cos^{2}\frac{2\pi}{3} = \left( - \frac{1}{2} \right)^{2} = \frac{1}{4};\]

\[4)\ a = \frac{4\pi}{3}:\]

\[\cos^{2}\frac{4\pi}{3} = \left( - \frac{1}{2} \right)^{2} = \frac{1}{4}.\]