sin(2x)=.1

I will assume that you want all values of x between 0 and 360 degrees

that means

you want all values of 2x between 0 and 720 degrees

2x=asin(0.1)

$$\underset{\,\,\,\,^{\textcolor[rgb]{0.66,0.66,0.66}{360^\circ}}}{{sin}}^{\!\!\mathtt{-1}}{\left({\mathtt{0.1}}\right)} = {\mathtt{5.739\: \!170\: \!477\: \!267^{\circ}}}$$

2x= 5.739 degrees,   365.739 degrees   OR    180-5.739=174.261,  174.261+360=534.261

$$x= \quad 2.87^0 \quad 182.87^0 \quad 87.13^0 \quad 267.13^0$$

$$\underset{\,\,\,\,^{\textcolor[rgb]{0.66,0.66,0.66}{360^\circ}}}{{sin}}{\left({\mathtt{2}}{\mathtt{\,\times\,}}{\mathtt{x}}\right)} = {\mathtt{0.1}} \Rightarrow {\mathtt{x}} = {\frac{{\mathtt{90}}{\mathtt{\,\times\,}}\underset{\,\,\,\,^{\textcolor[rgb]{0.66,0.66,0.66}{2\pi}}}{{sin}}^{\!\!\mathtt{-1}}{\left({\frac{{\mathtt{1}}}{{\mathtt{10}}}}\right)}}{{\mathtt{\pi}}}} \Rightarrow {\mathtt{x}} = {\mathtt{2.869\: \!585\: \!238\: \!646\: \!004\: \!1}}$$

Here's the (partial) graph of the solutions on [0, 360]...........https://www.desmos.com/calculator/hqatxdpan5