Question

Sin2x<1/2решите срочно​

Answer 1

Ответ:

sin2x=1/2

Упрощать здесь нечего, поэтому сразу начинаем решать по основной формуле

Пошаговое объяснение:

Откуда взялось П/6 ? это табличное значение: arcsin(1/2)=П/6

Answer 2

Okay, let's solve this inequality. We want to find the values of $x$ for which $\sin(2x) < \frac{1}{2}$.

Firstly, let's consider when $\sin(2x) = \frac{1}{2}$, as this is where the function equals the right side of the inequality.

$\sin(2x) = \frac{1}{2}$ when $2x = \frac{\pi}{6} + 2k\pi$ or $2x = \frac{5\pi}{6} + 2k\pi$, where $k$ is an integer.

Now, for $\sin(2x) < \frac{1}{2}$, $2x$ must be in the intervals between these values. So, we have:

$\frac{\pi}{6} + 2k\pi < 2x < \frac{5\pi}{6} + 2k\pi$

Divide all parts by 2:

$\frac{\pi}{12} + k\pi < x < \frac{5\pi}{12} + k\pi$

So, $x$ belongs to the intervals $(\frac{\pi}{12} + k\pi, \frac{5\pi}{12} + k\pi)$, where $k$ is an integer.

Hope this helps!