If $\sin (x)=\frac{3}{10}$ (in Quadrant-1), find
Give exact answers.
\[
\sin (2 x)=
\]

Step 1 ：We are given that \(\sin(x) = \frac{3}{10}\) and we are asked to find \(\sin(2x)\).

Step 2 ：We know that the formula for the double angle of sine is \(\sin(2x) = 2\sin(x)\cos(x)\).

Step 3 ：We can find \(\cos(x)\) using the Pythagorean identity \(\sin^2(x) + \cos^2(x) = 1\).

Step 4 ：Solving for \(\cos(x)\), we get \(\cos(x) = \sqrt{1 - \sin^2(x)} = \sqrt{1 - (\frac{3}{10})^2} = 0.9539392014169457\).

Step 5 ：Substituting both \(\sin(x)\) and \(\cos(x)\) into the formula for \(\sin(2x)\), we get \(\sin(2x) = 2 * \frac{3}{10} * 0.9539392014169457 = 0.5723635208501674\).

Step 6 ：So, the value of \(\sin(2x)\) is approximately \(\boxed{0.572}\).