Задание 16.2

Question

16.2. $^{\circ}$ Решите уравнение:
$$1) \sin x=\frac{1}{2};$$
$$2) \sin x=-\frac{\sqrt{2}}{2};$$
$$3) \sin x=\frac{\sqrt{5}}{3};$$
$$4) \sin x=1,5.$$

Gimli · Accepted Answer

1) $$\sin x=\frac{1}{2} $$
$$\quad x=(-1)^{n} \arcsin \frac{1}{2}+\pi n$$
$$x-(-1)^{n} \cdot \frac{\pi}{6}+\pi n$$
 2) $$\sin x=-\frac{\sqrt{2}}{2} $$
$$\quad x=(-1)^{n} \arcsin \left(-\frac{\sqrt{2}}{2}\right)+\pi n$$
$$x=(-1)^{n} \cdot\left(-\arcsin \frac{\sqrt{2}}{2}\right)+\pi n$$
$$x=(-1)^{n+1} \cdot \arcsin \frac{\sqrt{2}}{2}+\pi n$$
$$x=(-1)^{n+1} \cdot \frac{\pi}{4}+\pi n$$
3) $$\sin x=\frac{\sqrt{5}}{3} $$
$$x=(-1)^{n} \arcsin \frac{\sqrt{5}}{3}+\pi n$$
4) $$\sin x=1,5$$
$$ \quad x=(-1)^{n}\arcsin 1,5+\pi n$$

Задание 16.2

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Задание 16.2

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