If $\mathrm{sin}\left(x\right)=\frac{1}{2}=\mathrm{sin}\left(\frac{\pi}{6}\right)$, so:
$x}_{1}=\frac{\pi}{6$ $x}_{2}=5\frac{\pi}{6$, that has the same value $\left(\frac{1}{2}\right)$
Since $f\left(x\right)=\mathrm{sin}\left(x\right)$ is a periodic function, with period $2\pi$, there is an infinity if arcs that have the same sin value $\left(\frac{1}{2}\right)$, when the variable arc x rotates around the trig unit circle many times.
So,
$x=\frac{\pi}{6}+K\times 2\pi$; and $x=5\frac{\pi}{6}+K\times 2\pi$, where K is a whole number.

Jimmy Macias

Beginner2021-12-14Added 30 answers

$\mathrm{sin}30\xb0=\frac{1}{2}$ and $\mathrm{sin}150\xb0=\frac{1}{2}$