if sin x = -1 and x=[0,2pi] what is the value of x

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.

If sin x = -1 and x is in the interval [0, 2π], what is the value of x?

Solve the equation sin(x) = -1 in the interval [0, 2π] and find the value of x. This problem covers key trigonometric concepts, including the sine function and its behavior on the unit circle. Suitable for high school students in Grades 10-12.

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