The equation $\sin x = -1$ within the interval $[0, 2\pi]$ asks for the values of $x$ where the sine function equals -1.

The sine function reaches a value of -1 at the angle $x = \frac{3\pi}{2}$ (which is 270° in degrees).

Thus, the value of $x$ in the interval $[0, 2\pi]$ is:

$x = \frac{3\pi}{2}$

Would you like more details or have any questions? Here are 5 related questions to explore further:

1. What is the general solution to $\sin x = -1$ for all possible values of $x$?
2. How can the unit circle help determine the sine values for specific angles?
3. What are the properties of the sine function in different quadrants?
4. How can we solve $\sin x = k$ for arbitrary values of $k$?
5. What is the relationship between the sine and cosine functions?

Tip: The sine function has a period of $2\pi$, meaning it repeats every $2\pi$ units.