$x\approx \mathrm{0,358}+k\cdot 2\pi \vee x\approx \mathrm{2,784}+k\cdot 2\pi$

$x\approx \mathrm{-0,358}+k\cdot 2\pi \vee x\approx \mathrm{-2,784}+k\cdot 2\pi$

$x=\frac{1}{3}\pi +k\cdot 2\pi \vee x=\frac{2}{3}\pi +k\cdot 2\pi$

$x=1\frac{1}{4}\pi +k\cdot 2\pi \vee x=1\frac{3}{4}\pi +k\cdot 2\pi$

$x=\frac{1}{2}\pi +k\cdot 2\pi$

$x=1+k\cdot 2\pi \vee x=\pi -1+k\cdot 2\pi$

$x=sin\left(1\right)\approx \mathrm{0,841}$

$2sin\left(x\right)-1=0$ gives $sin\left(x\right)=\frac{1}{2}$ and so $x=\frac{1}{6}\pi \vee x=\frac{5}{6}\pi \vee x=2\frac{1}{6}\pi \vee x=2\frac{5}{6}\pi$.
The zeroes are $(\frac{1}{6}\pi ,0)$, $(\frac{5}{6}\pi ,0)$, $(2\frac{1}{6}\pi ,0)$ and $(2\frac{5}{6}\pi ,0)$.

$\frac{1}{6}\pi \le x\le \frac{5}{6}\pi \vee 2\frac{1}{6}\pi \le x\le 2\frac{5}{6}\pi$.

$sin\left(2x\right)=\mathrm{0,5}$ gives $2x=\frac{1}{6}\pi +k\cdot 2\pi \vee 2x=\frac{5}{6}\pi +k\cdot 2\pi$ and so $x=\frac{1}{12}\pi +k\cdot \pi \vee x=\frac{5}{12}\pi +k\cdot \pi$.
On $[0,4\pi ]$: $x=\frac{1}{12}\pi \vee x=\frac{5}{12}\pi \vee x=1\frac{1}{12}\pi \vee x=1\frac{5}{12}\pi \vee x=2\frac{1}{12}\pi \vee x=2\frac{5}{12}\pi \vee x=3\frac{1}{12}\pi \vee x=3\frac{5}{12}\pi$.

$\frac{1}{12}\pi \le x\le \frac{5}{12}\pi \vee 1\frac{1}{12}\pi \le x\le 1\frac{5}{12}\pi \vee 2\frac{1}{12}\pi \le x\le 2\frac{5}{12}\pi \vee 3\frac{1}{12}\pi \le x\le 3\frac{5}{12}\pi$.