If $\sin x=-1$ and $x \in[0,2 \pi]$, the value of $x$ is

Step 1 ：Given the equation \(\sin x = -1\) with \(x \in [0,2 \pi]\).

Step 2 ：The sine function reaches its minimum value of -1 at \(x = \frac{3\pi}{2}\) in the interval \([0, 2\pi]\).

Step 3 ：Therefore, the value of \(x\) that satisfies the equation \(\sin x = -1\) is \(x = \frac{3\pi}{2}\).

Step 4 ：Converting \(\frac{3\pi}{2}\) to decimal form gives approximately 4.71238898038469.

Step 5 ：Final Answer: The value of \(x\) that satisfies the equation \(\sin x = -1\) in the interval \([0, 2\pi]\) is \(\boxed{\frac{3\pi}{2}}\).