Решебник по алгебре и начала математического анализа 11 класс Колягин Задание 52

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

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

\[\sin\left( 2 \bullet \frac{\pi}{4} \right) = \sin\frac{\pi}{2} = 1;\]

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

\[\sin\frac{2\pi}{3} = \sin\frac{\pi}{3} = \frac{\sqrt{3}}{2};\]

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

\[\sin\left( - 2 \bullet \frac{2\pi}{3} \right) = \sin\left( - \frac{4\pi}{3} \right) =\]

\[= \sin\frac{2\pi}{3} = \frac{\sqrt{3}}{2};\]

\[4)\ a = - \frac{5\pi}{6}:\]

\[\sin\left( - 2 \bullet \frac{5\pi}{6} \right) = \sin\left( - \frac{5\pi}{3} \right) =\]

\[= \sin\frac{\pi}{3} = \frac{\sqrt{3}}{2}.\]