Задание 16.4

Question

16.4. $^{\circ}$ Решите уравнение:
$$1)\sin 2 x=\frac{\sqrt{2}}{2}$$
$$2)\sin \frac{x}{7}=0$$
$$3)\sin \frac{2 x}{5}=-\frac{\sqrt{3}}{2}$$

Gimli · Accepted Answer

1) $$\sin 2 x=\frac{\sqrt{2}}{2}$$
$$ \quad 2 x=(-1)^{n} \arcsin \frac{\sqrt{2}}{2}+\pi n$$
$$2 x=(-1)^{n} \cdot \frac{\pi}{4}+\pi n$$ 
$$x=(-1)^{n} \cdot \frac{\pi}{8}+\frac{\pi n}{2}, n\in \mathbb{Z}$$
2) $$\sin \frac{x}{7}=0$$
$$\frac{x}{7} = (-1)^n \arcsin 0 + \pi n$$
$$\frac{x}{7} = \pi n$$
$$x = 7\pi n, n\in \mathbb{Z}$$
3)$$\sin 2 x=-\frac{\sqrt{3}}{2}$$
$$\frac{2x}{5}=(-1)^{n} \arcsin (-\frac{\sqrt{3}}{2})+\pi n$$
$$\frac{2x}{5}=(-1)^{n}( -\arcsin \frac{\sqrt{3}}{2})+\pi n$$
$$\frac{2x}{5}=(-1)^{n} \frac{\pi}{3}+\pi n, n\in \mathbb{Z}$$

Задание 16.4

Answers

Comments

Задание 16.4

Answers

Comments

Add answer