Страница 131 номер 439, ГДЗ по алгебре за 10-11 класс Алимов - ответы и решение

1) \(\sin x = -1\)
\(x = -\dfrac{\pi}{2} + 2\pi k,\ k \in Z;\)

2) \(\cos x = -1\)
\(x = -\pi + 2\pi k,\ k \in Z;\)

3) \(\sin 3x = 0\)
\(3x = \pi k,\ k \in Z,\)
\(x = \dfrac{\pi}{3}k,\ k \in Z;\)

4) \(\cos 0{,}5x = 0\)
\(\dfrac{1}{2}x = \dfrac{\pi}{2} + \pi k,\ k \in Z,\)
\(x = \pi + 2\pi k,\ k \in Z;\)

5) \(\sin \left(\frac{x}{2} + \frac{2\pi}{3}\right) = 1\)
\(\dfrac{x}{2} + \dfrac{2\pi}{3} = \dfrac{\pi}{2} + 2\pi k,\ k \in Z,\)
\(\dfrac{x}{2} = -\dfrac{\pi}{6} + 2\pi k,\ k \in Z,\)
\(x = -\dfrac{\pi}{3} + 4\pi k,\ k \in Z;\)

6) \(\cos \left(5x + \frac{4\pi}{5}\right) = 1\)
\(5x + \dfrac{4\pi}{5} = 2\pi k,\ k \in Z,\)
\(5x = -\dfrac{4\pi}{5} + 2\pi k,\ k \in Z,\)
\(x = -\dfrac{4\pi}{25} + \dfrac{2\pi k}{5},\ k \in Z.\)